Publications 2019

Authors: Paul-Konstantin Oehlmann, Thorsten Schimannek

Preprint number: UUITP-53/19

Abstract: We present a novel technique to obtain base independent expressions for the matter loci of fibrations of complete intersection Calabi-Yau onefolds in toric ambient spaces. These can be used to systematically construct elliptically and genus one fibered Calabi-Yau d-folds that lead to desired gauge groups and spectra in F-theory. The technique, which we refer to as GV-spectroscopy, is based on the calculation of fiber Gopakumar-Vafa invariants using the Batyrev-Borisov construction of mirror pairs and application of the so-called Frobenius method to the data of a parametrized auxiliary polytope. In particular for fibers that generically lead to multiple sections, only multi-sections or that are complete intersections in higher codimension, our technique is vastly more efficient than classical approaches. As an application we study two Higgs chains of six-dimensional supergravities that are engineered by fibrations of codimension two complete intersection fibers. Both chains end on a vacuum with G=Z4 that is engineered by fibrations of bi-quadrics in P3. We use the detailed knowledge of the structure of the reducible fibers that we obtain from GV-spectroscopy to comment on the corresponding Tate-Shafarevich group. We also show that for all fibers the six-dimensional supergravity anomalies including the discrete anomalies generically cancel.

Authors: Aidan Herderschee, Song He, Fei Teng and Yong Zhang

Preprint number: UUITP-52/19

Abstract: We initiate the study of positive geometry and scattering forms for tree-level amplitudes with (massive) matter particles in (anti-)fundamental representation of color/flavor group. As a toy example, we study the bi-color scalar theory, which supplement the bi-adjoint theory with scalars in fundamental representations of both groups. Using a recursive construction we obtain a class of unbounded polytopes called open associahedra (or associahedra with certain facets at infinity) whose canonical form computes amplitudes in bi-color theory, for arbitrary number of legs and flavor assignments. 
In addition, we discuss the duality between color factors and wedge products, or ``color is kinematics”, for amplitudes with matter particles as well.

Authors: Vladimír Procházka, Alexander Söderberg

Preprint number: UUITP-51/19

We use renormalization group methods to study composite operators existing at a boundary of an interacting conformal field theory. By reinterpreting the boundary operator expansion as operator renormalization we relate the boundary conformal data to short-distance (near-boundary) divergences of bulk two-point functions. We clarify the difference between different regularization schemes and show that in the presence of boundary cutoff one can encounter power divergences implying additive renormalization of massive parameters akin to the divergences that appear in effective field theories with scalars. We further argue that in the presence of running couplings at the boundary the anomalous dimensions of certain composite operators can be computed from the relevant beta functions and remark on the implications for the boundary (pseudo) stress-energy tensor. The methods used in this paper can therefore serve as complement to the current boundary conformal bootstrap techniques in the regime where conformal symmetry is broken by quantum effects. We apply the formalism to a scalar field theory in $d=3-\epsilon$ with a quartic coupling at the boundary whose beta function we determine to the first non-trivial order. We study the operators in this theory and compute their conformal data using $\epsilon-$expansion at the Wilson-Fisher fixed point of the boundary renormalization group flow. We find that the model possesses a non-zero boundary stress-energy tensor and displacement operator both with vanishing anomalous dimensions. The boundary stress-energy tensor decouples at the fixed point in accordance with the Cardy's condition for conformal invariance. We end the main part of the paper by discussing the possible physical significance of this model for various values of $\epsilon$.

Authors: Arash Arabi Ardehali, Junho Hong, James T. Liu

Preprint number: UUITP-50/19

We study the Cardy-like 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 large-N limit after the Cardy-like limit and make a conjecture for the leading asymptotics of the index. While the Cardy-like 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 non-standard 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 non-standard solutions has a natural interpretation in terms of vacua of N=1* theory on R3×S1.

Authors: Arash Arabi Ardehali, Luca Cassia, Yongchao Lü

Preprint number: UUITP-49/19

We revisit the vacuum structure of the N=1 Intriligator-Seiberg-Shenker model on R3×S1. Guided by the Cardy-like asymptotics of its Romelsberger index, and building on earlier semi-classical results by Poppitz and Unsal, we argue that previously overlooked non-perturbative effects generate a Higgs-type potential on the classical Coulomb branch of the low-energy effective 3d N=2 theory. In particular, on part of the Coulomb branch we encounter the first instance of a dynamically-generated quintic monopole superpotential.

Authors: V. Del Duca, S. Druc, J. M. Drummond, C. Duhr, F. Dulat, R. Marzucca, G. Papathanasiou, B. Verbeek

Preprint Number: UUITP-48/19

Abstract: We propose an all-loop expression for scattering amplitudes in planar N = 4 super Yang-Mills theory in multi-Regge 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 all-order extension for the central emission vertex that we recently computed at next-to-leading logarithmic accuracy. As an application, we use our all-order formula to prove that all amplitudes in this theory in multi-Regge kinematics are single-valued multiple polylogarithms of uniform transcendental weight.

Authors: Gregor Kälin, Gustav Mogull, Alexander Ochirov, and Bram Verbeek

Preprint number: UUITP-47/19

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
full-color two-loop four-gluon 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 integrand-level 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
full-color two-loop four-point amplitudes with both matter and vectors on external legs
in which lower-weight terms also cancel using an appropriate IR scheme. This provides
us with values for the two-loop cusp, gluonic, and quark anomalous dimensions in N = 2
supersymmetric QCD, which are cross-checked between the three different amplitudes.

Authors: Gregor Kälin, Rafael Porto

Preprint number:  UUITP-46/19

Abstract: We recently introduced in [1910.03008] a "boundary-to-bound" dictionary between gravitational scattering data and observables for bound states of non-spinning 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 Post-Minkowskian (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 PM-expanded 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 two-loops. Agreement is found in the overlap between PM and Post-Newtonian (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 aligned-spin contributions, with J the (canonical) total angular momentum. Explicit checks are performed to display perfect agreement using state-of-the-art PN results in the literature. Using the map between test- and two-body dynamics, we also compute the periastron advance up to quadratic order in the spin, to one-loop 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".

Authors: Jan E. Gerken, Axel Kleinschmidt, Oliver Schlotterer

Preprint number: UUITP--45/19

We investigate generating functions for the integrals over world-sheet tori appearing in closed-string one-loop amplitudes of bosonic, heterotic and type-II theories. These closed-string integrals are shown to obey homogeneous and linear differential equations in the modular parameter of the torus. We spell out the first-order Cauchy--Riemann and second-order Laplace equations for the generating functions for any number of external states. The low-energy expansion of such torus integrals introduces infinite families of non-holomorphic modular forms known as modular graph forms. Our results generate homogeneous first- and second-order differential equations for arbitrary such modular graph forms and can be viewed as a step towards all-order low-energy expansions of closed-string integrals.

Authors: Nikolay Gromov, Fedor Levkovich-Maslyuk, Paul Ryan, Dmytro Volin

Preprint-number: UUITP-44/19

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 higher-rank 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 Q-functions and their dual.

Authors: Adam Bzowski, Paul McFadden, Kostas Skenderis

Preprint-number: UUITP-43/19

We provide a Feynman integral representation for the general momentum-space scalar 4-point 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 momentum-space conformal cross-ratios. It involves three integrations over momenta (i.e., is 3-loop 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.

Authors: Agnese Bissi, Parijat Dey, Tobias Hansen

Preprint-number: UUITP-42/19

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 Wilson-Fisher fixed point is computed in closed form to order epsilon^2 in the epsilon expansion.

Authors: Alessandro Bombini, Giulia Fardelli

Preprint number:  UUITP-41/19

Abstract: We study  holographic entanglement entropy and  holographic complexity in a two-charge, 1/4-BPS 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. 

Authors: Gregor Kälin and Rafael Porto

Preprint number:  UUITP-40/19

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 Post-Minkowskian (PM) expansion. Our map relies on remarkable connections between the relative momentum of the two-body 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 two-loop orders. We also provide closed-form expressions for the orbital frequency and periastron advance at tree-level and one-loop order, respectively, which capture a series of exact terms in the Post-Newtonian expansion. We  then perform a partial PM resummation, using a no-recoil approximation for the amplitude. This limit is behind the map between the scattering angle for a test-particle and the two-body dynamics to 2PM. We show that it also captures a subset of higher order terms beyond the test-particle 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.

Authors: Luca Cassia, Rebecca Lodin, Aleksandr Popolitov, Maxim Zabzine

Preprint number:  UUITP-39/19

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 Yang-Mills-Chern-Simons U(N) theory on the squashed sphere S3b with one adjoint chiral and two antichiral fundamental multiplets, for specific values of Chern-Simons level κ2 and Fayet-Illiopoulos 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.

Authors: Alex Edison, Encrio Herrmann, Julio Parra-Martinez, Jaroslav Trnka

Preprint number:  UUITP-38/19

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 multi-particle unitarity cuts for asymptotically large momenta and expose an improved UV behavior of four-dimensional 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 non-trivial 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 Yang-Mills theory. We also show how the behavior at infinity is related to the scaling of tree-level amplitudes under certain multi-line chiral shifts which can be used to construct new recursion relations

Authors: Pinaki Banerjee and Parijat Dey

Preprint number:  UUITP-37/19

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.

Authors: Carlos R. Mafra and Oliver Schlotterer

Preprint number: UUITP--36/19

We study generating functions of moduli-space integrals at genus one that are expected to form a basis for massless n-point one-loop amplitudes of open superstrings and open bosonic strings. These integrals are shown to satisfy the same type of linear and homogeneous first-order differential equation w.r.t. the modular parameter tau which is known from the A-elliptic Knizhnik-Zamolodchikov-Bernard associator. The expressions for their tau-derivatives take a universal form for the integration cycles in planar and non-planar one-loop open-string amplitudes. These differential equations manifest the uniformly transcendental appearance of iterated integrals over holomorphic Eisenstein series in the low-energy 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 non-planar integrals is manifestly expressible in terms of iterated Eisenstein integrals without referring to twisted elliptic multiple zeta values. The degeneration of the moduli-space integrals at tau -> i infinity is expressed in terms of their genus-zero analogues -- (n+2)-point Parke-Taylor integrals over disk boundaries. Our results yield a compact formula for alpha'-expansions of n-point integrals over boundaries of cylinder- or Möbius-strip worldsheets, where any desired order is accessible from elementary operations.

Authors:  Zvi Bern, John Joseph Carrasco, Marco Chiodaroli, Henrik Johansson, Radu Roiban

Preprint number: UUITP-35/19

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 loop-level calculations, the broad web of theories linked by the duality and the associated double-copy 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.

Authors: Carlos R. Mafra, Oliver Schlotterer

Preprint number: UUITP-34/19

We present a new method to evaluate the alpha'-expansion of genus-one integrals over open-string punctures and unravel the structure of the elliptic multiple zeta values in its coefficients. This is done by obtaining a simple differential equation of Knizhnik--Zamolodchikov--Bernard-type 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 genus-zero integrals.

Authors: Yongchao Lü and Joseph A. Minahan

Preprint number:  UUITP-33/19

Abstract: We consider anomaly cancellation for $SU(N)\times SU(2)\times U(1)$ gauge theories where the left-handed chiral multiplets are in higher $SU(2)$ representations.  In particular,  if the left-handed 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 Mordell-Weil theorem, Mazur's theorem and the Cremona elliptic curve database which uses Kolyvagin's theorem on the Birch Swinnerton-Dyer conjecture to prove these statements.

Authors:  Nikolay Bobev, Pieter Bomans, Friðrik Freyr Gautason, Joseph A. Minahan and Anton Nedelin 

Preprint number: UUITP-32/19

Authors: Francesco Bonechi, Alberto S. Cattaneo, Jian Qiu, Maxim Zabzine

Preprint number: UUITP-31/19

Abstract: We study an equivariant extension of the Batalin-Vilkovisky 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 Yang-Mills in 2d and of Donaldson-Witten theory.

Authors: J. Boehm, W. Decker, A. Georgoudis, F. J. Pfreundt, M. Rahn, P. Wasser, Y. Zhang

Preprint number: UUITP-30/19

Abstract: We introduce an algebro-geometrically motived integration-by-parts (IBP) reduction method for multi-loop and multi-scale 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 GPI-space, 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 Petri-nets. We demonstrate the potential of our method at the nontrivial example of reducing two-loop five-point nonplanar double-pentagon integrals. We also use GPI-space to convert the basis of IBP reductions, and discuss the possible simplification of IBP coefficients in the uniformly transcendental basis. 

Authors: Tommi Tenkanen and Luca Visinelli

Preprint number: UUITP-29/19

Abstract: In order to accommodate the QCD axion as the dark matter (DM) in a model in which the Peccei-Quinn (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 non-minimally 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 self-coupling $\lambda_\phi = 0.1$, which correspond to the PQ breaking scale $v_\sigma \gtrsim 10^{14}\,$GeV and tensor-to-scalar 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.

Authors: Luca Visinelli, Sunny Vagnozzi, Ulf Danielsson

Preprint number: UUITP-28/19

Abstract: Persisting tensions between high-redshift and low-redshift 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 low-redshift 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 high-redshift and low-redshift data persist with future data, it would be worth reconsidering and further refining our toy negative cosmological constant model.

Authors: Souvik Banerjee, Ulf Danielsson, Giuseppe Dibitetto, Suvendu Giri, Marjorie Schillo

Preprint number: UUITP-26/19

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 non-supersymmetric AdS vacua must decay, we discuss the alternative possibility of realizing an effective four-dimensional dS cosmology on a codimension-one 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 non-perturbative decay and is embedded in a five-dimensional bulk in a time-dependent way. In this paper we discuss the relation between this scenario and the weak gravity conjecture and further develop the details of the four-dimensional 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 four-dimensional matter  arises from a string cloud in the bulk, and we examine the consequences for the particle mass spectrum. Furthermore, we show how effective four-dimensional Einstein gravity on the bubble is obtained from  the five-dimensional Gauss equation. We conclude by outlining some implications that this paradigm will have for holography, inflation, the standard model, and black holes.

Authors: Song He, Fei Teng, Yong Zhang

Preprint number: UUITP-25/19

Abstract: We further elaborate on the general construction proposed in~\cite{He:2018pol}, which connects, via tree-level double copy, massless string amplitudes with color-ordered QFT amplitudes that are given by Cachazo-He-Yuan formulas. The current paper serves as a detailed study of the integration-by-parts procedure for any tree-level 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 Yang-Mills-scalar 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 Parke-Taylor 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 closed-form result for such multitrace amplitudes and thus greatly extends our result for the single-trace case. As a byproduct, it gives a new CHY formula for all Yang-Mills-scalar amplitudes. We also study consistency checks of the formula such as factorizations on massless poles.

Authors: Henrik Johansson, Alexander Ochirov

Preprint number: UUITP-24/19

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 gauge-group 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 black-hole scattering and gravitational waves. Our construction benefits from making the little group explicit for the massive particles, as shown on lower-point 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 vector-scalar couplings. We find new gauge-invariant double-copy formulae for tree-level amplitudes with two distinct-flavor pairs of matter and any number of gravitons. These are similar to, but inherently different from, the well-known Kawai-Lewellen-Tye formulae, since the latter only hold for the double copy of purely adjoint gauge theories.

Authors: Eleonora Di Valentino, Ricardo Z. Ferreira, Luca Visinelli, Ulf Danielsson

Preprint number: UUITP-23/19

Abstract: We consider a quintessence field which transitions from a matter-like 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.

Author: Gang Chen, Henrik Johansson, Fei Teng, Tianheng Wang

Preprint number: UUITP-22/19

Abstract: The duality between color and kinematics present in scattering amplitudes
of Yang-Mills 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 four-dimensional 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 dimension-agnostic notation

and determine the kinematic algebra valid up to certain O (ε i ·ε j ) 2 terms that in four
dimensions compute the next-to-MHV sector involving two scalars. The kinematic
algebra in this sector is simple, given that we introduce tensor currents that generalize
standard Yang-Mills 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
Yang-Mills theory.

Authors: Antonio Pittelli, Michelangelo Preti

Preprint Number: UUITP-21/19

Authors: Adam Bzowski and Marjorie Schillo

Preprint Number: UUITP-20/19

Abstract: In this work, we present a holographic renormalization scheme for asymptotically anti-de 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 long-standing 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

Authors: Pietro Longhi, Fabrizio Nieri, Antonio Pittelli 

Preprint Number: UUITP-19/19

Abstract: We consider 4d N=1 gauge theories with R-symmetry 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 Robin-like. 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 three-torus, for which we derive explicit 1-loop determinants.We consider 4d N=1 gauge theories with R-symmetry 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 Robin-like. 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 three-torus, for which we derive explicit 1-loop determinants.

Authors: Magdalena Larfors and Robin Schneider

Preprint number: UUITP-18/19

We analyse line bundle cohomologies on all favourable co-dimension 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.

Authors: Guido Festuccia, Jian Qiu, Jacob Winding, and Maxim Zabzine

Preprint number: UUITP-16/19

Authors: Aleksandra Anokhina, Alexei Morozov and Aleksandr Popolitov

Preprint number: UUITP-15/19

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 thick-knot domain is further stratified. For thin knots evolution is governed by the standard T-deformation λ of the eigenvalues of the R-matrix. Emerging in the thick knots regions are additionalLyapunov exponents, which are multiples of thenaive ones. Such frequency doubling is typical for non-linear dynamics, and our observation can signal about a hidden non-linearityof superpolynomial evolution. Since evolution with eigenvalues λ^2, . . . , λ^g is ”faster” than the one with λ in the thin-knot region, we name it “nimble”.

Authors: Claude Duhr, Henrik Johansson, Gregor Kälin, Gustav Mogull, and Bram Verbeek

Preprint number: UUITP-14/19

Abstract: We present the fully integrated form of the two-loop four-gluon 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 super-Yang-Mills theory, except that now certain lower-weight terms appear. We comment on the corresponding results for other gauge groups.

Authors: Giuseppe Dibitetto and Nicolò Petri

Preprint Number: UUITP-13/19

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 D2-D4-NS5-D6-D8 brane intersection. We provide a particular supergravity solution in 10d describing this bound state and we discuss the relations between its near-horizongeometry 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.

Authors: Xenia de la Ossa, Magdalena Larfors, Matthew Magill, Eirik E. Svanes

Preprint Number: UUITP-12/19

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.

Authors: Chris Hull and Ulf Lindström

Preprint number: UUITP-11/19

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. 

Authors : Souvik Banerjee, Julius Engelsoy, Jorge Larana-Aragon, Bo Sundborg, Larus Thorlacius, Nico Wintergerst.  

Preprint number : UUITP-10/19

A macroscopic version of Einstein-Podolsky-Rosen 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 post-quench 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 post-quench free field theory share interesting properties with correlators in strongly coupled systems.

Author: K. Zarembo

Preprint number: UUITP-9/19 

Relatively low crossover temperature suggests that chiral symmetry restoration in QCD may well be described within the low-energy effective theory. The shape of the pseudocritical line in the T-mu plane is estimated within this assumption. No critical endpoint is found for physical values of quark masses.

Authors: Usman Naseer, Barton Zwiebach

Preprint number: UUITP-8/19

We apply recently developed convex programs to  find the minimal-area 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 well-known 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

Authors: Souvik Banerjee, Kyriakos Papadodimas, Suvrat Raju, Prashant Samantray, Pushkal Shrivastava

Preprint number: UUITP-7/19

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 high-order loop diagrams. We also consider holographic theories in d-spacetime dimensions where we show that the leading two-point function of generalized free-fields 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.

Authors: Johan Blåbäck, Ulf Danielsson, Giuseppe Dibitetto, Suvendu Giri

Preprint number: UUITP-6/19

We consider dimensional reductions of M-theory 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 non-supersymmetric 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 no-scale 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.

Authors: Christian Marboe, Erik Widen

Preprint number: UUITP-5/19

We investigate the solution space of the β-deformed Quantum Spectral Curve by studying a sample of solutions corresponding to single-trace operators that in the undeformed theory belong to the Konishi multiplet. We discuss how to set the precise boundary conditions for the leading Q-system for a given state, how to solve it, and how to build perturbative corrections to the Pμ-system. We confirm and add several loop orders to known results in the literature.

Author: Vladimir Prochazka

Preprint number: UUITP-4/19

Abstract: We consider the two-point functions of conserved bulk currents and energy-momentum 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 form-factor. 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 non-local form resembling the standard anomaly-induced term in a two-dimensional CFT at small $p_n$ and Chern-Simons 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 three-dimensional fermion. In particular we manage to obtain the respective anomalies via a diagrammatic momentum space computation and expose the well-known relation between bulk parity anomaly and boundary gauge anomalies.

Author: Arash Arabi Ardehali

Preprint number: UUITP-3/19

Choi, Kim, Kim, and Nahmgoong have recently pioneered analyzing a Cardy-like 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 Cardy-like 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 saddle-point, 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.