Publikationer 2019

Asymptotic growth of the 4d N=4 index and partially deconfined phases
Authors: Arash Arabi Ardehali, Junho Hong, James T. Liu
Preprint number: UUITP50/19
We study the Cardylike asymptotics of the 4d N=4 index and demonstrate the existence of partially deconfined phases where the asymptotic growth of the index is not as rapid as in the fully deconfined case. We then take the largeN limit after the Cardylike limit and make a conjecture for the leading asymptotics of the index. While the Cardylike behavior is derived using the integral representation of the index, we demonstrate how the same results can be obtained using the Bethe ansatz type approach as well. In doing so, we discover new nonstandard solutions to the elliptic Bethe ansatz equations including continuous families of solutions for SU(N) theory with N≥3. We argue that the existence of both standard and continuous nonstandard solutions has a natural interpretation in terms of vacua of N=1* theory on R3×S1.

From Exact Results to Gauge Dynamics on R3×S1
Authors: Arash Arabi Ardehali, Luca Cassia, Yongchao Lü
Preprint number: UUITP49/19
We revisit the vacuum structure of the N=1 IntriligatorSeibergShenker model on R3×S1. Guided by the Cardylike asymptotics of its Romelsberger index, and building on earlier semiclassical results by Poppitz and Unsal, we argue that previously overlooked nonperturbative effects generate a Higgstype potential on the classical Coulomb branch of the lowenergy effective 3d N=2 theory. In particular, on part of the Coulomb branch we encounter the first instance of a dynamicallygenerated quintic monopole superpotential.

Allorder amplitudes at any multiplicity in the multiRegge limit
Authors: V. Del Duca, S. Druc, J. M. Drummond, C. Duhr, F. Dulat, R. Marzucca, G. Papathanasiou, B. Verbeek
Preprint Number: UUITP48/19
Abstract: We propose an allloop expression for scattering amplitudes in planar N = 4 super YangMills theory in multiRegge kinematics valid for all multiplicities, all helicity configurations and arbitrary logarithmic accuracy. Our expression is arrived at from comparing explicit perturbative results with general expectations from the integrable structure of a closely related collinear limit. A crucial ingredient of the analysis is an allorder extension for the central emission vertex that we recently computed at nexttoleading logarithmic accuracy. As an application, we use our allorder formula to prove that all amplitudes in this theory in multiRegge kinematics are singlevalued multiple polylogarithms of uniform transcendental weight.

Infrared and transcendental structure of twoloop supersymmetric QCD amplitudes
Authors: Gregor Kälin, Gustav Mogull, Alexander Ochirov, and Bram Verbeek
Preprint number: UUITP47/19
Abstract: Using a careful choice of infrared (IR) subtraction scheme, we demonstrate
the cancellation of all terms with transcendental weights 0,1,2 from the finite part of the
fullcolor twoloop fourgluon N = 2 supersymmetric QCD amplitude, with N f massless
supersymmetric quarks. This generalizes the previously observed cancellation of weight
2 terms in the superconformal theory, where N f = 2N c for gauge group SU(N c ). The
subtraction scheme follows naturally both from general IR factorization principles and
from an integrandlevel analysis of divergences in this amplitude. The divergences are
written in terms of scalar triangle integrals whose expressions are known to all orders in
the dimensional regulator = (4 − D)/2. We also present integrated expressions for the
fullcolor twoloop fourpoint amplitudes with both matter and vectors on external legs
in which lowerweight terms also cancel using an appropriate IR scheme. This provides
us with values for the twoloop cusp, gluonic, and quark anomalous dimensions in N = 2
supersymmetric QCD, which are crosschecked between the three different amplitudes. 
From Boundary Data to Bound States II: Scattering Angle to Dynamical Invariants (with Twist)
Authors: Gregor Kälin, Rafael Porto
Preprint number: UUITP46/19
Abstract: We recently introduced in [1910.03008] a "boundarytobound" dictionary between gravitational scattering data and observables for bound states of nonspinning bodies. In this paper, we elaborate further on this (holographic) map. We start by deriving the following  remarkably simple  formula relating the periastron advance to the scattering angle: ΔΦ(J,E)=χ(J,E)+χ(−J,E), via analytic continuation in angular momentum and binding energy. Using explicit expressions from [1910.03008], we confirm its validity to all orders in the PostMinkowskian (PM) expansion. Furthermore, we reconstruct the radial action for the bound state directly from the knowledge of the scattering angle. The radial action enables us to write compact expressions for dynamical invariants in terms of the deflection angle to all PM orders, which can also be written as a function of the PMexpanded amplitude. As an example, we reproduce our result in [1910.03008] for the periastron advance, and compute the radial and azimuthal frequencies and redshift variable to twoloops. Agreement is found in the overlap between PM and PostNewtonian (PN) schemes. Last but not least, we initiate the study of our dictionary including spin. We demonstrate that the same relation between deflection angle and periastron advance applies for alignedspin contributions, with J the (canonical) total angular momentum. Explicit checks are performed to display perfect agreement using stateoftheart PN results in the literature. Using the map between test and twobody dynamics, we also compute the periastron advance up to quadratic order in the spin, to oneloop and to all orders in velocity. We conclude with a discussion on the generalized "impetus formula" for spinning bodies and black holes as "elementary particles".

Allorder differential equations for oneloop closedstring integrals and modular graph forms
Authors: Jan E. Gerken, Axel Kleinschmidt, Oliver Schlotterer
Preprint number: UUITP45/19
We investigate generating functions for the integrals over worldsheet tori appearing in closedstring oneloop amplitudes of bosonic, heterotic and typeII theories. These closedstring integrals are shown to obey homogeneous and linear differential equations in the modular parameter of the torus. We spell out the firstorder CauchyRiemann and secondorder Laplace equations for the
generating functions for any number of external states. The lowenergy expansion of such torus integrals introduces infinite families of nonholomorphic modular forms known as modular graph forms. Our results generate homogeneous first and secondorder differential equations for arbitrary such modular graph forms and can be viewed as a step towards allorder lowenergy expansions of closedstring integrals. 
Dual Separated Variables and Scalar Products
Authors: Nikolay Gromov, Fedor LevkovichMaslyuk, Paul Ryan, Dmytro Volin
Preprintnumber: UUITP44/19
Separation of variables (SoV) is an extremely efficient and elegant technique for analysing physical systems but its application to integrable spin chains was limited until recently to the simplest su(2) cases. In this paper we continue developing the SoV program for higherrank spin chains and demonstrate how to derive the measure for the su(3) case. Our results are a natural consequence of factorisability of the wave function and functional orthogonality relations following from the interplay between Baxter equations for Qfunctions and their dual.

Conformal 4point functions in momentum space
Authors: Adam Bzowski, Paul McFadden, Kostas Skenderis
Preprintnumber: UUITP43/19
We provide a Feynman integral representation for the general momentumspace scalar 4point function in any conformal field theory. This representation solves the conformal Ward identities and features an arbitrary function of two variables which play the role of momentumspace conformal crossratios. It involves three integrations over momenta (i.e., is 3loop like), though in certain cases the number of integrations reduces to two or one. We identify the special values of the operator and spacetime dimensions for which singularities arise leading to anomalies and beta functions. Several illustrative examples from perturbative field theory and holography are discussed.

Dispersion Relation for CFT FourPoint Functions
Authors: Agnese Bissi, Parijat Dey, Tobias Hansen
Preprintnumber: UUITP42/19
We present a dispersion relation in conformal field theory which expresses the four point function as an integral over its single discontinuity. Exploiting the analytic properties of the OPE and crossing symmetry of the correlator, we show that in perturbative settings the correlator depends only on the spectrum of the theory, as well as the OPE coefficients of certain low twist operators, and can be reconstructed unambiguously. In contrast to the Lorentzian inversion formula, the validity of the dispersion relation does not assume Regge behavior and is not restricted to the exchange of spinning operators. As an application, the correlator < phi phi phi phi> in phi^4 theory at the WilsonFisher fixed point is computed in closed form to order epsilon^2 in the epsilon expansion.

Holographic entanglement entropy and complexity ofmicrostate geometries
Authors: Alessandro Bombini, Giulia Fardelli
Preprint number: UUITP41/19
Abstract: We study holographic entanglement entropy and holographic complexity in a twocharge, 1/4BPS family of solutions of type IIB supergravity, controlled by one dimensionless parameter. All the geometries in this family are asymptotically AdS3 x S3 x T4 and, varying the parameter that controls them, they interpolate between the global AdS3 x S3 x T4 and the massless BTZ3 x S3 x T4 geometry. Due to AdS/CFT duality, these geometries are dual to pure CFT heavy states.
We find that there is no emergence of entanglement shadow for all the values of the parameter and we discuss the relation with the massless BTZ result, underlying the relevance of the nature of the dual states.
We also compute the holographic complexity of formation of these geometries, finding a nice monotonic function that interpolates between the pure AdS3 result and the massless BTZ one. 
From Boundary Data to Bound States
Authors: Gregor Kälin and Rafael Porto
Preprint number: UUITP40/19
Abstract: We introduce a — somewhat holographic — dictionary between gravitational observables for scattering processes (measured at the boundary) and adiabatic invariants for bound orbits (in the bulk), to all orders in the PostMinkowskian (PM) expansion. Our map relies on remarkable connections between the relative momentum of the twobody problem, the classical limit of the scattering amplitude and the deflection angle in hyperbolic motion. These relationships allow us to compute observables for generic closed orbits (such as the periastron advance ∆Φ) via a radial action depending only on boundary data, through analytic continuation. A simplified (more geometrical) map can be obtained for circular orbits, enabling us to extract the orbital frequency as a function of the (conserved) binding energy, Ω(E), directly from scattering information. As an example, using the results in Bern et al. [1901.04424, 1908.01493], we readily derive Ω(E) and ∆Φ(J, E) to twoloop orders. We also provide closedform expressions for the orbital frequency and periastron advance at treelevel and oneloop order, respectively, which capture a series of exact terms in the PostNewtonian expansion. We then perform a partial PM resummation, using a norecoil approximation for the amplitude. This limit is behind the map between the scattering angle for a testparticle and the twobody dynamics to 2PM. We show that it also captures a subset of higher order terms beyond the testparticle limit. While a (rather lengthy) Hamiltonian may be derived as an intermediate step, our map applies directly between gauge invariant quantities. Our findings provide a starting point for an alternative approach to the binary problem. We conclude with future directions and some speculations on the classical double copy.

Exact SUSY Wilson loops on S3 from qVirasoro constraints
Authors: Luca Cassia, Rebecca Lodin, Aleksandr Popolitov, Maxim Zabzine
Preprint number: UUITP39/19
Abstract: Using the ideas from the BPS/CFT correspondence, we give an explicit recursive formula for computing supersymmetric Wilson loop averages in 3d N=2 YangMillsChernSimons U(N) theory on the squashed sphere S3b with one adjoint chiral and two antichiral fundamental multiplets, for specific values of ChernSimons level κ2 and FayetIlliopoulos parameter κ1. For these values of κ1 and κ2 the north and south pole turn out to be completely independent, and therefore Wilson loop averages factorize into answers for the two constituent D2×S1 theories. In particular, our formula provides results for the theory on the round sphere when the squashing is removed.

Gravity loop integrands from the ultraviolet
Authors: Alex Edison, Encrio Herrmann, Julio ParraMartinez, Jaroslav Trnka
Preprint number: UUITP38/19
Abstract: We demonstrate that loop integrands of (super)gravity scattering amplitudes possess surprising properties in the ultraviolet (UV) region. In particular, we study the scaling of multiparticle unitarity cuts for asymptotically large momenta and expose an improved UV behavior of fourdimensional cuts through seven loops as compared to standard expectations. For N=8 supergravity, we show that the improved large momentum scaling combined with the behavior of the integrand under BCFW deformations of external kinematics uniquely fixes the loop integrands in a number of nontrivial cases. In the integrand construction, all scaling conditions are homogeneous. Therefore, the only required information about the amplitude is its vanishing at particular points in momentum space. This homogeneous construction gives indirect evidence for a new geometric picture for graviton amplitudes similar to the one found for planar N=4 super YangMills theory. We also show how the behavior at infinity is related to the scaling of treelevel amplitudes under certain multiline chiral shifts which can be used to construct new recursion relations

Analytic Bootstrap for Logarithmic CFT
Authors: Pinaki Banerjee and Parijat Dey
Preprint number: UUITP37/19
Abstract: We study logarithmic conformal field theory (LogCFT) in four dimensions using conformal bootstrap techniques in the large spin limit. We focus on the constraints imposed by conformal symmetry on the four point function of certain logarithmic scalar operators and compute the leading correction to the anomalous dimension of double trace operators in the large spin limit. There exist certain holographic duals to such LogCFTs, which involve higher derivative equations of motion. The anomalous dimension is related to the binding energy of a state where two scalars rotate around each other with a large angular momentum. We compute this energy shift and compare it to the anomalous dimension of the large spin double trace operators due to stress tensor exchange in the LogCFT. Our result shows that the cluster decomposition principle is satisfied for LogCFTs as long as the dimensions of the operators are positive.

Oneloop openstring integrals from differential equations: allorder alpha'expansions at n points
Authors: Carlos R. Mafra and Oliver Schlotterer
Preprint number: UUITP36/19
We study generating functions of modulispace integrals at genus one that are expected to form a basis for massless npoint oneloop amplitudes of open superstrings and open bosonic strings. These integrals are shown to satisfy the same type of linear and homogeneous firstorder differential equation w.r.t. the modular parameter tau which is known from the Aelliptic KnizhnikZamolodchikovBernard associator. The expressions for their tauderivatives take a universal form for the integration cycles in planar and nonplanar oneloop openstring amplitudes. These differential equations manifest the uniformly transcendental appearance of iterated integrals over holomorphic Eisenstein series in the lowenergy expansion w.r.t. the inverse string tension alpha'. In fact, we are led to matrix representations of certain derivations dual to Eisenstein series. Like this, also the alpha'expansion of nonplanar integrals is manifestly expressible in terms of iterated Eisenstein integrals without referring to twisted elliptic multiple zeta values. The degeneration of the modulispace integrals at tau > i infinity is expressed in terms of their genuszero analogues  (n+2)point ParkeTaylor integrals over disk boundaries. Our results yield a compact formula for alpha'expansions of npoint integrals over boundaries of cylinder or Möbiusstrip worldsheets, where any desired order is accessible from elementary operations.

The Duality Between Color and Kinematics and its Applications
Authors: Zvi Bern, John Joseph Carrasco, Marco Chiodaroli, Henrik Johansson, Radu Roiban
Preprint number: UUITP35/19
Abstract: This review describes the duality between color and kinematics and its applications, with the aim of gaining a deeper understanding of the perturbative structure of gauge and gravity theories. We emphasize, in particular, applications to looplevel calculations, the broad web of theories linked by the duality and the associated doublecopy structure, and the issue of extending the duality and double copy beyond scattering amplitudes. The review is aimed at doctoral students and junior researchers both inside and outside the field of amplitudes and is accompanied by various exercises.

Allorder alpha'expansion of oneloop openstring integrals
Authors: Carlos R. Mafra, Oliver Schlotterer
Preprint number: UUITP34/19
We present a new method to evaluate the alpha'expansion of genusone integrals over openstring punctures and unravel the structure of the elliptic multiple zeta values in its coefficients. This is done by obtaining a simple differential equation of KnizhnikZamolodchikovBernardtype satisfied by generating functions of such integrals, and solving it via Picard iteration. The initial condition involves the generating functions at the cusp tau > i infty and can be reduced to genuszero integrals.

Notes on anomalies, elliptic curves and the BSD conjecture
Authors: Yongchao Lü and Joseph A. Minahan
Preprint number: UUITP33/19
Abstract: We consider anomaly cancellation for $SU(N)\times SU(2)\times U(1)$ gauge theories where the lefthanded chiral multiplets are in higher $SU(2)$ representations. In particular, if the lefthanded quarks and leptons transform under the triplet representation of $SU(2)$ and if the $U(1)$ gauge group is compact then up to an overall scaling there is only one possible nontrivial assignment for the hypercharges if $N=3$, and two if $N=9$. Otherwise there are infinitely many. We use the MordellWeil theorem, Mazur's theorem and the Cremona elliptic curve database which uses Kolyvagin's theorem on the Birch SwinnertonDyer conjecture to prove these statements.

Supersymmetric YangMills, Spherical Branes, and Precision Holography
Authors: Nikolay Bobev, Pieter Bomans, Friðrik Freyr Gautason, Joseph A. Minahan and Anton Nedelin
Preprint number: UUITP32/19
Using supersymmetric localization we compute the free energy and BPS Wilson loop vacuum expectation values for planar maximally supersymmetric Yang Mills theory on S^d in the strong coupling limit for 2 ≤ d < 6. The same calculation can also be performed in supergravity using the recently found spherical brane solutions. We find excellent agreement between the two sets of results. This constitutes a nontrivial precision test of holography in a non conformal setting. The free energy of maximal SYM on S^6 diverges in the strong coupling limit which might signify the onset of little string theory. We show how this divergence can be regularized both in QFT and in supergravity. We also consider d = 7 with a small negative ’t Hooft coupling and show that the free energy and Wilson loop vacuum expectation value agree with the results from supergravity after addressing some subtleties.

Equivariant BatalinVilkovisky formalism
Authors: Francesco Bonechi, Alberto S. Cattaneo, Jian Qiu, Maxim Zabzine
Preprint number: UUITP31/19
Abstract: We study an equivariant extension of the BatalinVilkovisky formalism for quantizing gauge theories. Namely, we introduce a general framework to encompass failures of the quantum master equation, and we apply it to the natural equivariant extension of AKSZ solutions of the classical master equation (CME). As examples of the construction, we recover the equivariant extension of supersymmetric YangMills in 2d and of DonaldsonWitten theory.

Integrationbyparts reductions of Feynman integrals using Singular and GPISpace
Authors: J. Boehm, W. Decker, A. Georgoudis, F. J. Pfreundt, M. Rahn, P. Wasser, Y. Zhang
Preprint number: UUITP30/19
Abstract: We introduce an algebrogeometrically motived integrationbyparts (IBP) reduction method for multiloop and multiscale Feynman integrals, using a framework for massively parallel computations in computer algebra. This framework combines the computer algebra system Singular with the workflow management system GPIspace, which is being developed at the Fraunhofer Institute for Industrial Mathematics (ITWM). In our approach, the IBP relations are first trimmed by modern algebraic geometry tools and then solved by sparse linear algebra and our new interpolation methods. These steps are efficiently automatized and automatically parallelized by modeling the algorithm in GPI space using the language of Petrinets. We demonstrate the potential of our method at the nontrivial example of reducing twoloop fivepoint nonplanar doublepentagon integrals. We also use GPIspace to convert the basis of IBP reductions, and discuss the possible simplification of IBP coefficients in the uniformly transcendental basis.

Axion dark matter from Higgs inflation with an intermediate $H_*$
Authors: Tommi Tenkanen and Luca Visinelli
Preprint number: UUITP29/19
Abstract: In order to accommodate the QCD axion as the dark matter (DM) in a model in which the PecceiQuinn (PQ) symmetry is broken before the end of inflation, a relatively low scale of inflation has to be invoked in order to avoid bounds from DM isocurvature fluctuations. We construct a simple model in which the Standard Model Higgs field is nonminimally coupled to gravity and acts as the inflaton, leading to a scale of inflation $H_* \sim 10^8\,$GeV. When the PQ symmetry is incorporated in the model and the energy scale at which the symmetry breaks is much larger than the scale of inflation, we find that in this scenario the required axion mass for which the axion constitutes all DM is $m_0 \lesssim 0.05{\rm \,\mu eV}$ for a quartic Higgs selfcoupling $\lambda_\phi = 0.1$, which correspond to the PQ breaking scale $v_\sigma \gtrsim 10^{14}\,$GeV and tensortoscalar ratio $r \sim 10^{12}$. Future experiments sensitive to the relevant QCD axion mass scale can therefore shed light on the physics of the Universe before the end of inflation.

Revisiting the case for a negative cosmological constant from lowredshift data
Authors: Luca Visinelli, Sunny Vagnozzi, Ulf Danielsson
Preprint number: UUITP28/19
Abstract: Persisting tensions between highredshift and lowredshift precision cosmological observations suggest the dark energy sector of the Universe might be more complex than the positive cosmological constant of the $\Lambda$CDM model, and in particular might have a negative energy density. Motivated by string theory considerations, wherein consistent AdS background are ubiquitous, we explore a scenario where the dark energy sector consists of two components: a negative cosmological constant, on top of which we consider a dark energy component with equation of state $w_{\phi}$. We test the consistency of the model against lowredshift Baryon Acoustic Oscillation and Type Ia Supernovae distance measurements, assessing two alternative choices of distance anchors: the sound horizon at baryon drag $r_{\rm drag}$ as determined by the \textit{Planck} collaboration, and the Hubble constant $H_0$ as determined by the SH0ES program. While a negative cosmological constant remains perfectly consistent with data, we find no evidence for the former, while we find mild indications for an effective phantom dark energy component on top, regardless of the choice of distance anchor. A model comparison analysis performed through the Akaike information criterion reveals the $\Lambda$CDM model is favoured over our negative cosmological constant model. While our results are inconclusive, should tensions between highredshift and lowredshift data persist with future data, it would be worth reconsidering and further refining our toy negative cosmological constant model.

de Sitter Cosmology on an expanding bubble
Authors: Souvik Banerjee, Ulf Danielsson, Giuseppe Dibitetto, Suvendu Giri, Marjorie Schillo
Preprint number: UUITP26/19
Abstract: Constructing an explicit compactification yielding a metastable de Sitter (dS) vacuum in a UV consistent string theory is an incredibly difficult open problem. Motivated by this issue, as well as the conjecture that all nonsupersymmetric AdS vacua must decay, we discuss the alternative possibility of realizing an effective fourdimensional dS cosmology on a codimensionone bubble wall separating two AdS5 vacua. The construction further elaborates on the scenario of arXiv:1807.01570, where the aforementioned cosmology arises due to a nonperturbative decay and is embedded in a fivedimensional bulk in a timedependent way. In this paper we discuss the relation between this scenario and the weak gravity conjecture and further develop the details of the fourdimensional cosmology. We provide a bulk interpretation for the dS temperature as the Unruh temperature experienced by an accelerated observer riding the bubble. A source of fourdimensional matter arises from a string cloud in the bulk, and we examine the consequences for the particle mass spectrum. Furthermore, we show how effective fourdimensional Einstein gravity on the bubble is obtained from the fivedimensional Gauss equation. We conclude by outlining some implications that this paradigm will have for holography, inflation, the standard model, and black holes.

String Correlators: Recursive Expansion, IntegrationbyParts and Scattering Equations
Authors: Song He, Fei Teng, Yong Zhang
Preprint number: UUITP25/19
Abstract: We further elaborate on the general construction proposed in~\cite{He:2018pol}, which connects, via treelevel double copy, massless string amplitudes with colorordered QFT amplitudes that are given by CachazoHeYuan formulas. The current paper serves as a detailed study of the integrationbyparts procedure for any treelevel massless string correlator outlined in the previous letter. We present two new results in the context of heterotic and (compactified) bosonic string theories. First, we find a new recursive expansion of any multitrace mixed correlator in these theories into a logarithmic part corresponding to the CHY integrand for YangMillsscalar amplitudes, plus correlators with the total number of traces and gluons decreased. By iterating the expansion, we systematically reduce string correlators with any number of subcycles to linear combination of ParkeTaylor factors and similarly for the case with gluons. Based on this, we then derive a CHY formula for the corresponding $(DF)^2 + {\rm YM} + \phi^3$ amplitudes. It is the first closedform result for such multitrace amplitudes and thus greatly extends our result for the singletrace case. As a byproduct, it gives a new CHY formula for all YangMillsscalar amplitudes. We also study consistency checks of the formula such as factorizations on massless poles.

Double copy for massive quantum particles with spin
Authors: Henrik Johansson, Alexander Ochirov
Preprint number: UUITP24/19
Abstract: The duality between color and kinematics was originally observed for purely adjoint massless gauge theories, and later found to hold even after introducing massive fermionic and scalar matter in arbitrary gaugegroup representations. Such a generalization was critical for obtaining both loop amplitudes in pure Einstein gravity and realistic gravitational matter from the double copy. In this paper we elaborate on the double copy that yields amplitudes in gravitational theories coupled to flavored massive matter with spin, which is relevant to the problems of blackhole scattering and gravitational waves. Our construction benefits from making the little group explicit for the massive particles, as shown on lowerpoint examples. For concreteness, we focus on the double copy of QCD with massive quarks, for which we work out the gravitational Lagrangian up to quartic scalar and vectorscalar couplings. We find new gaugeinvariant doublecopy formulae for treelevel amplitudes with two distinctflavor pairs of matter and any number of gravitons. These are similar to, but inherently different from, the wellknown KawaiLewellenTye formulae, since the latter only hold for the double copy of purely adjoint gauge theories.

Late time transitions in the quintessence field and the $H_0$ tension
Authors: Eleonora Di Valentino, Ricardo Z. Ferreira, Luca Visinelli, Ulf Danielsson
Preprint number: UUITP23/19
Abstract: We consider a quintessence field which transitions from a matterlike to a cosmological constant behavior between recombination and the present time. We aim at easing the tension in the measurement of the present Hubble rate, and we assess the $\Lambda$CDM model properly enlarged to include our quintessence field against cosmological observations. The model does not address the scope we proposed, so we comment on the explanations for this. This result allows us to exclude a class of quintessential models in view of the current tension over different measurements of the Hubble rate.

On the kinematic algebra for BCJ numerators beyond the MHV sector
Author: Gang Chen, Henrik Johansson, Fei Teng, Tianheng Wang
Preprint number: UUITP22/19
Abstract: The duality between color and kinematics present in scattering amplitudes
of YangMills theory strongly suggest the existence of a hidden kinematic Lie algebra
that controls the gauge theory. While associated BCJ numerators are known on closed
forms to any multiplicity at tree level, the kinematic algebra has only been partially
explored for the simplest of fourdimensional amplitudes: up to the MHV sector. In this
paper we introduce a framework that allows us to characterize the algebra beyond the
MHV sector. This allows us to both constrain some of the ambiguities of the kinematic
algebra, and better control the generalized gauge freedom that is associated with the
BCJ numerators. Specifically, in this paper, we work in dimensionagnostic notation
and determine the kinematic algebra valid up to certain O (ε i ·ε j ) 2 terms that in four
dimensions compute the nexttoMHV sector involving two scalars. The kinematic
algebra in this sector is simple, given that we introduce tensor currents that generalize
standard YangMills vector currents. These tensor currents controls the generalized
gauge freedom, allowing us to generate multiple different versions of BCJ numerators
from the same kinematic algebra. The framework should generalize to other sectors in
YangMills theory. 
Integrable Fishnet from γDeformed N = 2 Quivers
Authors: Antonio Pittelli, Michelangelo Preti
Preprint Number: UUITP21/19
We propose the γdeformation of fourdimensional N = 2 quiver gauge theories, obtained by applying the LuninMaldacena deformation with respect to the U(1)r × SU(2)R Rsymmetry. The resulting theory is supplied with doubletrace counterterms and has a nontrivial RGflow. We com pute the oneloop βfunction and identify the conformal fixed points of these theories. Furthermore, we study the doublescaling limit of large imaginary γ and weak ’t Hooft coupling. In this regime, both gauge fields and hypermultiplets decouple, leaving a nonsupersymmetric, nongauge theory where gluinos and vector multiplet scalars interact via Yukawa couplings. This model is integrable even though the original N = 2 theory is not. Indeed, the anomalous dimension of the BMN vac uum is dominated by fermionic wheel graphs, whose bulk constitutes an integrable fishnet known as brickwall domain. Finally, we compute this scaling dimension to leading order directly from Feynman diagrams both for the general γdeformation and the doublescaled theory.

Dimensional regularization for holographic RG flows
Authors: Adam Bzowski and Marjorie Schillo
Preprint Number: UUITP20/19
Abstract: In this work, we present a holographic renormalization scheme for asymptotically antide Sitter spacetimes in which the dual renormalization scheme of the boundaryfield theory is dimensional regularization. This constitutes a new level of precision in theholographic dictionary and paves the way for the exact matching of scheme dependent quantities, such as holographic beta functions, with field theory computations. Furthermore,the renormalization procedure identifies a local source field which satisfies the equations ofmotion along renormalization group flows, resolving a longstanding puzzle regarding theWilsonian coupling in holography. This identification of the source field also provides newinsight into field theories deformed by marginal operators, which have been traditionallydifficult to analyze due to altered bulk asymptotics. Finally, we demonstrate a new relation equating the analyticity of the holographic beta function to the absence of conformalanomalies, and conjecture that the conformal anomaly should vanish in the UV for allholographic constructions

Localization of 4d N=1 theories on D2 x T2
Authors: Pietro Longhi, Fabrizio Nieri, Antonio Pittelli
Preprint Number: UUITP19/19
Abstract: We consider 4d N=1 gauge theories with Rsymmetry on a hemisphere times a torus. We apply localization techniques to evaluate the exact partition function through a cohomological reformulation of the supersymmetry transformations. Our results represent the natural elliptic lifts of the lower dimensional analogs as well as a field theoretic derivation of the conjectured 4d holomorphic blocks, from which partition functions of compact spaces with diverse topology can be recovered through gluing. We also analyze the different boundary conditions which can naturally be imposed on the chiral multiplets, which turn out to be either Dirichlet or Robinlike. We show that different boundary conditions are related to each other by coupling the bulk to 3d N=1 degrees of freedom on the boundary threetorus, for which we derive explicit 1loop determinants.We consider 4d N=1 gauge theories with Rsymmetry on a hemisphere times a torus. We apply localization techniques to evaluate the exact partition function through a cohomological reformulation of the supersymmetry transformations. Our results represent the natural elliptic lifts of the lower dimensional analogs as well as a field theoretic derivation of the conjectured 4d holomorphic blocks, from which partition functions of compact spaces with diverse topology can be recovered through gluing. We also analyze the different boundary conditions which can naturally be imposed on the chiral multiplets, which turn out to be either Dirichlet or Robinlike. We show that different boundary conditions are related to each other by coupling the bulk to 3d N=1 degrees of freedom on the boundary threetorus, for which we derive explicit 1loop determinants.

Line bundle cohomologies on CICYs with Picard number two
Authors: Magdalena Larfors and Robin Schneider
Preprint number: UUITP18/19
We analyse line bundle cohomologies on all favourable codimension two Complete Intersection Calabi Yau (CICY) manifolds of Picard number two. Our results provide further evidence that the cohomology dimensions of such line bundles are given by analytic expressions, which change between regions in the line bundle charge space. This agrees with recent observations of CY line bundles presented in Refs [1,2]. In many cases, the expressions for bundle cohomology dimensions are polynomial functions of the line bundle charges (of degree at most 3), and the regions are cones. A more novel observation is that for some CICY manifolds, the cohomologies are more succinctly determined by recursive relationships. There can also be boundaries between regions where a polynomial fit fails, and we link these exceptional cases to irregular behaviour of the index of the line bundle. Finally, our observations provide evidence for similarities in the line bundle cohomologies for CICY manifolds that share rows in the configuration matrix. Among such related CICY manifolds, we find both that the line bundle charge space is partitioned in the same manner, and that the same, or closely related, analytical descriptions apply for the cohomology dimensions in these regions.

Metastable Vacua in LargeN QCD3
Authors: Adi Armoni, Thomas T. Dumitrescu, Guido Festuccia, and Zohar Komargodski
Preprint number: UUITP17/19
We reexamine the vacuum structure of threedimensional quantum chromodynamics (QCD_3) with gauge group SU(N), N_f fundamental quark flavors, and a levelk ChernSimons term. This analysis can be reliably carried out in the largeN, fixed N_f, k limit of the theory, up to certain assumptions that we spell out explicitly. At leading order in the largeN expansion we find N_f + 1 distinct, exactly degenerate vacuum superselection sectors with different patterns of flavorsymmetry breaking. The associated massless NambuGoldstone bosons are generically accompanied by topological ChernSimons theories. This set of vacua contains many candidate phases previously proposed for QCD_3. At subleading order in the largeN expansion, the exact degeneracy between the different superselection sectors is lifted, leading to a multitude of metastable vacua. If we dial the quark masses, different metastable vacua can become the true vacuum of the theory, leading to a sequence of firstorder phase transitions. This intricate largeN dynamics can be captured by the previously proposed bosonic dual theories for QCD_3, provided these bosonic duals are furnished with a suitable scalar potential. Interestingly, this potential must include terms beyond quartic order in the scalar fields.

Transversally Elliptic Complex and Cohomological Field Theory
Authors: Guido Festuccia, Jian Qiu, Jacob Winding, and Maxim Zabzine
Preprint number: UUITP16/19
This work is a continuation of our previous paper arXiv:1812.06473 where we have constructed N = 2 supersymmetric YangMills theory on 4D manifolds with a Killing vector field with isolated fixed points. In this work we expand on the mathematical as pects of the theory, with a particular focus on its nature as a cohomological field theory. The wellknown DonaldsonWitten theory is a twisted version of N = 2 SYM and can also be constructed using the AtiyahJeffrey construction [1]. This theory is concerned with the moduli space of antiselfdual gauge connections, with a deformation theory controlled by an elliptic complex. More generally, supersymmetry requires considering configurations that look like either instantons or antiinstantons around fixed points, which we call flipping instantons. The flipping instantons of our 4D N = 2 theory are derived from the 5D contact instantons. The novelty is that their deformation the ory is controlled by a transversally elliptic complex, which we demonstrate here. We repeat the AtiyahJeffrey construction in the equivariant setting and arrive at the La grangian (an equivariant Euler class in the relevant field space) that was also obtained from our previous work arXiv:1812.06473. We show that the transversal ellipticity of the deformation complex is crucial for the nondegeneracy of the Lagrangian and the calculability of the theory. Our construction is valid on a large class of quasi toric 4 manifolds.

Nimble evolution for pretzel Khovanov polynomials
Authors: Aleksandra Anokhina, Alexei Morozov and Aleksandr Popolitov
Preprint number: UUITP15/19
Abstract: We conjecture explicit evolution formulas for Khovanov polynomials for pretzel knots in some regions in the windings space.Our description is exhaustive for genera 1 and 2. As previously observed, evolution at T/=−1 is not fully smooth: it switchesabruptly at the boundaries between different regions. We reveal that this happens also at the boundary between thin and thickknots, moreover, the thickknot domain is further stratified. For thin knots evolution is governed by the standard Tdeformation λ of the eigenvalues of the Rmatrix. Emerging in the thick knots regions are additionalLyapunov exponents, which are multiples of thenaive ones. Such frequency doubling is typical for nonlinear dynamics, and our observation can signal about a hidden nonlinearityof superpolynomial evolution. Since evolution with eigenvalues λ^2, . . . , λ^g is ”faster” than the one with λ in the thinknot region, we name it “nimble”.

The FullColor TwoLoop FourGluon Amplitude in N = 2 SuperQCD
Authors: Claude Duhr, Henrik Johansson, Gregor Kälin, Gustav Mogull, and Bram Verbeek
Preprint number: UUITP14/19
Abstract: We present the fully integrated form of the twoloop fourgluon amplitude in N=2 supersymmetric quantum chromodynamics with gauge group SU(Nc) and with Nf massless supersymmetric quarks (hypermultiplets) in the fundamental representation. Our result maintains full dependence on Nc and Nf , and relies on the existence of a compact integrand representation that exhibits the duality between color and kinematics. Specializing to the N=2 superconformal theory, where Nf = 2Nc , we obtain remarkably simple amplitudes that have an analytic structure close to that of N=4 superYangMills theory, except that now certain lowerweight terms appear. We comment on the corresponding results for other gauge groups.

AdS3 vacua and surface defects in massive IIA
Authors: Giuseppe Dibitetto and Nicolò Petri
Preprint Number: UUITP13/19
Abstract: We summarize the results and the ideas in [1–3] where new warped AdS3 backgrounds are derived in massive IIA string theory by uplifting exact solutions in N=1,d=7 and N= (1,1), d=6 gauged supergravities. These solutions are respectively asymptotically AdS7 and AdS6 and theyare related to the D2D4NS5D6D8 brane intersection. We provide a particular supergravity solution in 10d describing this bound state and we discuss the relations between its nearhorizongeometry and the uplifts from 6d and 7d. Then we give the holographic interpretations of these AdS3 warped backgrounds in terms of N= (0,4) defect SCFT2 within the N= (1,0) SCFT6 and the N=2 SCFT5.

Superpotential of Three Dimensional N=1 Heterotic Supergravity
Authors: Xenia de la Ossa, Magdalena Larfors, Matthew Magill, Eirik E. Svanes
Preprint Number: UUITP12/19
Abstract: We dimensionally reduce the ten dimensional heterotic action on spacetimes of the form M(2,1)×Y, where M(2,1) is three dimensional maximally symmetric Anti de Sitter or Minkowski space, and Y is a compact seven dimensional manifold with G2 structure. In doing so, we derive the real superpotential functional of the corresponding three dimensional N=1 theory. We confirm that extrema of this functional precisely correspond to supersymmetric heterotic compactifications on manifolds of G2 structure. We make some comments on the role of the superpotential functional with respect to the coupled moduli problem of instanton bundles over G2 manifolds.

Strong Kähler with Torsion as Generalised Geometry
Authors: Chris Hull and Ulf Lindström
Preprint number: UUITP11/19
Abstract: Strong Kähler with Torsion is the target space geometry of (2,1) and (2,0) supersymmetric nonlinear sigma models. We discuss how it can be represented in terms of Generalised Complex Geometry in analogy to the Gualtieri map from the geometry of (2,2) supersymmetric nonlinear sigma modelsto Generalised Kähler Geometry.

Quenched coupling, entangled equilibria, and correlated composite operators: a tale of two O(N) models
Authors : Souvik Banerjee, Julius Engelsoy, Jorge LaranaAragon, Bo Sundborg, Larus Thorlacius, Nico Wintergerst.
Preprint number : UUITP10/19
A macroscopic version of EinsteinPodolskyRosen entanglement is obtained by quenching a linear coupling between two O(N) vector models. A quench of the mixed vacuum produces an excited entangled state, reminiscent of puried thermal equilibrium, whose properties can be studied analytically in the free limit of the individual field theories. The decoupling of different wavelength modes in free field theory prevents true thermalisation but a more subtle difference is that the density operator obtained by a partial trace does not commute with the postquench Hamiltonian. Approximately thermal behaviour is obtained in the limit of weak initial mixing and a smooth but rapid quench. More surprisingly, late time correlation functions of composite operators in the postquench free field theory share interesting properties with correlators in strongly coupled systems.

Chiral Estimate of QCD Pseudocritical Line
Author: K. Zarembo
Preprint number: UUITP9/19
Relatively low crossover temperature suggests that chiral symmetry restoration in QCD may well be described within the lowenergy effective theory. The shape of the pseudocritical line in the Tmu plane is estimated within this assumption. No critical endpoint is found for physical values of quark masses.

Isosystolic extremal metrics with multiple bands of crossing geodesics
Authors: Usman Naseer, Barton Zwiebach
Preprint number: UUITP8/19
We apply recently developed convex programs to find the minimalarea Riemannian metric on $2n$sided polygons ($n\geq 3$) with length conditions on curves joining opposite sides. We argue that the Riemannian extremal metric coincides with the conformal extremal metric on the regular $2n$gon. The case $n=3$ was considered by Calabi. The region covered by the maximal number $n$ of geodesics bands extends over most of the surface and exhibits positive curvature. As $n\to \infty$ the metric, away from the boundary, approaches the wellknown round extremal metric on $\mathbb{RP}_2$. We extend Calabi's isosystolic variational principle to the case of regions with more than three bands of systolic geodesics. The extremal metric on $\mathbb{RP}_2$ is a stationary point of this functional applied to a surface with infinite number of systolic bands

A Bound on Thermal Relativistic Correlators at Large Spacelike Momenta
Authors: Souvik Banerjee, Kyriakos Papadodimas, Suvrat Raju, Prashant Samantray, Pushkal Shrivastava
Preprint number: UUITP7/19
We consider thermal Wightman correlators in a relativistic quantum field theory in the limit where the spatial momenta of the insertions become large while their frequencies stay fixed. We show that, in this limit, the size of this correlator is bounded by exp(βR) where R is the radius of the smallest sphere that contains the polygon formed by the momenta. We argue that, generically, perturbative quantum field theories can saturate this bound through suitably highorder loop diagrams. We also consider holographic theories in dspacetime dimensions where we show that the leading twopoint function of generalized freefields in such theories saturates the bound in d = 2 and is below the bound for d > 2. We briefly discuss interactions in holographic theories and conclude with a discussion of several open problems.

Constructing stable de Sitter in Mtheory from higher curvature corrections
Authors: Johan Blåbäck, Ulf Danielsson, Giuseppe Dibitetto, Suvendu Giri
Preprint number: UUITP6/19
We consider dimensional reductions of Mtheory on T⁷/ℤ₂³ with the inclusion of arbitrary metric flux and spacetime filling KK monopoles. With these ingredients at hand, we are able to construct a novel family of nonsupersymmetric yet tachyon free Minkowski extrema. These solutions are supported by pure geometry with no extra need for gauge fluxes and possess a fully stable perturbative mass spectrum, up to a single flat direction. Such a direction corresponds to the overall internal volume, with respect to which the scalar potential exhibts a noscale behavior. We then provide a mechanism that lifts the flat direction to give it a positive squared mass while turning Mkw₄ into dS₄ The construction makes use of the combined effect of G₇ flux and higher curvature corrections. Our solution is scale separated and the qunatum corrections are small. Finally we speculate on novel possibilities when it comes to scale hierarchies within a given construction of this type, and possible issues with the choice of quantum vacuum.

The fate of the Konishi multiplet in the βdeformed Quantum Spectral Curve
Authors: Christian Marboe, Erik Widen
Preprint number: UUITP5/19
We investigate the solution space of the βdeformed Quantum Spectral Curve by studying a sample of solutions corresponding to singletrace operators that in the undeformed theory belong to the Konishi multiplet. We discuss how to set the precise boundary conditions for the leading Qsystem for a given state, how to solve it, and how to build perturbative corrections to the Pμsystem. We confirm and add several loop orders to known results in the literature.

Boundary gauge and gravitational anomalies from Ward identities
Author: Vladimir Prochazka
Preprint number: UUITP4/19
Abstract: We consider the twopoint functions of conserved bulk currents and energymomentum tensor in a boundary CFT defined on $\mathbb{R}_^{1,2}$. Starting from the consistent forms of boundary gauge and gravitational anomalies we derive their respective contributions to the correlation functions in the form of anomalous Ward identities. Using the recently developed momentum space formalism we find an anomalous solution to each of these identities depending on a single undetermined formfactor. We study the solution in two different kinematic limits corresponding to small and large momentum $p_n$, perpendicular to the boundary. We find that the anomalous term interpolates between a nonlocal form resembling the standard anomalyinduced term in a twodimensional CFT at small $p_n$ and ChernSimons contact terms at large $p_n$. Using this we derive some consistency conditions regarding the dependence of these anomalies on the boundary conditions and discuss possible cancellation mechanisms. These ideas are then demonstrated on the explicit example of free, massless threedimensional fermion. In particular we manage to obtain the respective anomalies via a diagrammatic momentum space computation and expose the wellknown relation between bulk parity anomaly and boundary gauge anomalies.

Cardylike asymptotics of the 4d N=4 index and AdS_5 blackholes
Author: Arash Arabi Ardehali
Preprint number: UUITP3/19
Choi, Kim, Kim, and Nahmgoong have recently pioneered analyzing a Cardylike limit of the superconformal index of the 4d N=4 theory with complexified fugacities which encodes the entropy of the dual supersymmetric AdS_5 blackholes. Here we study the Cardylike asymptotics of the index within the rigorous framework of elliptic hypergeometric integrals, thereby filling a gap in their derivation of the blackhole entropy function, finding a new blackhole saddlepoint, and demonstrating novel bifurcation phenomena in the asymptotics of the index as a function of fugacity phases. We also comment on the relevance of the supersymmetric Casimir energy to the blackhole entropy function in the present context.

Branes, partition functions and quadratic monopole superpotentials
Authors: Antonio Amariti, Luca Cassia, Ivan Garozzo, Noppadol Mekareeya
Preprint number: UUITP2/19
We obtain the brane setup describing 3d N=2 dualities for USp(2Nc) and U(Nc) SQCD with monopole superpotentials. This classification follows from a complete analysis of affine and twisted affine compactifications from 4d. The analysis leads to a new duality for the unitary case that has been previously overlooked in the literature. We check this by matching of the three sphere partition function of the two sides of this new duality and find a perfect agreement. Furthermore we use the partition function to predict new 3d N=2 dualities for SQCD with monopole superpotentials and tensorial matter.

N = 2* Phase Transitions and Holography
Authors: Jorge G. Russo, Erik Widen, Konstantin Zarembo
Preprint number: UUITP1/19
We clarify the relationship between probe analysis of the supergravity dual and the largeN solution of the localization matrix model for the planar N = 2* superYangMills theory. A formalism inspired by supergravity allows us to systematically solve the matrix model at strong coupling. Quite surprisingly, we find that quantum phase transitions, known to occur in the N = 2* theory, start to be visible at the third order of the strongcoupling expansion and thus constitute a perturbative phenomenon on the string worldsheet.