Publikationer 2019

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.

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.