Monday

Amihay Hanany

Branes and Higgs branches in 5d and 6d. This talks reviews the recent exciting results on Higgs branches in higher dimensions. After a long period of neglect, the structure which arises from Higgs branches turns out to be surprising, rich, and full of new physics phenomena. In six dimensions the well known small instanton transition turns out to be a geometric notion known as a transverse slice. This is augmented with a new phenomenon that arises each time a string becomes tension less — discrete gauging. In five dimensions there is a rich structure of SQCD theories which depends on the number of colors, Nc, flavors, Nf, and CS level k. Of course branes play a central role and lead to a beautiful picture which derives and tests these new results!

Schlomo Razamat

Pure glue in six dimensions and quivers in four dimensions. We study compactifications on Riemann surfaces with punctures of N=(1,0) 6d SCFTs with a one dimensional tensor branch and no continuous global symmetries. The effective description of such models on the tensor branch is in terms of pure gauge theories with decoupled tensor. For generic Riemann surfaces, the resulting theories in four dimensions are expected to have N=1 supersymmetry. We compute the anomalies expected from the resulting 4d theories by integrating the anomaly polynomial of the 6d theory on the Riemann surface. For the cases with 6d gauge models with gauge groups SU(3) and SO(8) we further propose a field theory construction for the resulting 4d theories. For the 6d SU(3) theory, we argue that the theories in four dimensions are quivers with SU(3) gauge nodes and free chiral fields. The theories one obtains from the 6d SO(8) gauge theory are quivers with SU(4) gauge groups and chiral fields with R charge a half. In the last case the theories constructed for general Riemann surfaces involve gauging of symmetries appearing at strong coupling. The conformal manifolds of the models are constructed from gauge couplings and baryonic superpotentials. We support our conjectures by matching the dimensions of the conformal manifolds with complex structure moduli of the Riemann surfaces, matching anomalies between six and four dimensions, and checking the dualities related to different pair of pants decompositions of the surfaces. As a simple application of the results we conjecture that SU(3) gauge theory with nine flavors in four dimensions has a duality group acting on the seven dimensional conformal manifold which is the mapping class group of sphere with ten marked points.

Alberto Lerda

Surface operators and duality relations in N=2 gauge theories. I discuss the non-perturbative properties of half-BPS surface operators in N=2 gauge theories in four dimensions from two distinct points of view: i) as monodromy defects with ramified instantons, and ii) as coupled 2d/4d quiver theories, and show how these two descriptions are related to each other by studying the properties of the twisted superpotential that governs the low-energy dynamics on the surface defects. I also discuss the non-perturbative duality relations which connect distinct ultraviolet quiver theories that have the same infrared behaviour and thus describe the same surface operator using different degrees of freedom. I will argue that, from the localization point of view, these different dual realizations correspond to different choices of integration prescriptions in the ramified instanton partition function.

Yuta Sekiguchi

Extended Gauge Theory Deformations From Flux Backgrounds. We consider supersymmetric deformations of gauge theories in various dimensions obtained from a String Theory realisation of branes embedded in flux backgrounds. In particular we obtain deformations which take the form of Wilson line defects, where the R-symmetry is twisted into the gauge symmetry. Furthermore, we construct higher-order generalisations, also including a twisting of the R-symmetry, that have symmetries expectedly associated to co-dimension two and three defects.

Luigi Tizzano

Exploring 5D Supersymmetric RG Flows. I will present a new curved supersymmetric background which can be used to define a 5D supersymmetric index which is well defined for non-conformal theories. I will also comment on various applications of the index such as the connection with 4D Schur index, the IR description of 5D BPS particles and the role of instanton operators.

Andreas Gerhardus

Supersymmetric Sigma Models: Dualities and Quantum Geometry. Two-dimensional N=(2,2) supersymmetric gauged linear sigma models are a rich area of research for both physics and mathematics. They offer a powerful framework to study string compactifications and display far reaching connections to geometry. Moreover, they exhibit interesting gauge theory dynamics such as strong coupling phases and dualities. In this talk, based on research in collaboration with Hans Jockers, I will connect the above aspects to supersymmetric gauge theory observables and modern localization techniques. In particular, I will explain how gauged linear sigma model correlation functions encode the target space quantum cohomology, and discuss a non-Abelian strong-weak coupling duality supported by the match of two-sphere partition functions.

Keita Nii

Exact results in 3d N=2 Spin(7) gauge theories. I explain three-dimensional N=2 Spin(7) gauge theories with spinorial matters and vectorial matters. The quantum Coulomb branch on the moduli space of vacua is one- or two-dimensional depending on the matter contents. For particular values of (Nf,NS), we find s-confinement phases and derive exact superpotentials. The 3d dynamics of Spin(7) is connected to the 4d dynamics via KK-monopoles. Along the Higgs branch of the Spin(7) theories, we obtain 3d N=2 G2 or SU(4) theories and some of them lead to new s-confinement phases.

Tuesday

Massimo Bianchi

On marginal deformations of SCFT's in \(D=3\) and their \(\mathrm{AdS}_4\) duals. We analyse exactly marginal deformations of N=4 supersymmetric AdS4 vacua of Type IIB string theory with localized 5-brane sources and their holographic dual 3d quiver gauge theories. We exploit gauged supergravity, and the representations of the relevant superconformal algebra to classify the short multiplets containing the marginal N=2 deformations associated to the chiral rings of the Higgs and Coulomb branches, and discuss mixed-branch operators. We identify the origin of these moduli in string theory, matching the operators of the chiral rings with open strings on the magnetized 5-brane sources thus giving support to the holographic duality in this context.

Carlo Angelantonj

Strings and Magnetic Fields. I shall present the dynamics of open strings in the presence of closed and open magnetic field backgrounds. These backgrounds are conjectured to play an important role in the perturbative dynamics of supersymmetric gauge theories and, moreover, could connect to topological amplitudes.

Chris Hull

Non-geometric Calabi-Yau Backgrounds in String Theory. String theory duality symmetries can be used to glue together different patches of a solution to construct what have been called ‘non-geometric spaces’; these can be good solutions of string theory even though they would not be allowed in supergravity. In this talk, some recent work with Israel and Sarti will be described that constructs non-geometric analogues of Calabi-Yau manifolds in which patches are glued together with mirror symmetry transformations to construct a ‘mirrorfold'. These solutions preserve the same amount of supersymmetry as Calabi-Yau spaces, but typically have far fewer light moduli and so lead to models with far fewer light particles.

Raphaël Belliard

Topological recursion for Nekrasov partition functions through the AGT correspondence. The AGT correspondence relates Nekrasov partition functions in the omega-background to Toda conformal blocks with non vanishing background charges. In this talk we will review a recently developed method to solve the Ward identities satisfied by those conformal blocks, using the topoogical recursion procedure applied to an emerging quantum spectral curve in the heavy charge limit. This is based on the joint work arXiv:1801.03433 with Bertrand Eynard.

Jun Nian

Localization of 4d N=1 Gauge Theories and Dualities. In this talk we discuss the supersymmetric localization of 4d N=1 gauge theories on \(S^2 \times \mathbb{R}^2\) and compute their partition functions. The results are related to the partition functions of 4d N=1 gauge theories on the Omega background with two epsilon parameters, which can be viewed as building blocks of the Nekrasov partition functions of the 4d N=2 theories on the Omega background. As an application, we use the N=1 partition functions to test various dualities such as the 4d Seiberg duality. Further applications to the 4d Argyres-Douglas theories and the generalized AGT relation will also be discussed.

Antoine Bourget

The Importance of Being Disconnected. We introduce gauge theories based on a class of disconnected gauge groups, called principal extensions. These groups implement in a consistent way the discrete gauging of charge conjugation, for arbitrary rank. Focusing on the principal extension of SU(N), we explain how many of the exact methods for theories with 8 supercharges can be put into practice in that context. We then explore the physical consequences of having a disconnected gauge group: we find that the Coulomb branch is generically non-freely generated, and the global symmetry of the Higgs branch is modified in a non-trivial way.

Alessandro Pini

4d N=3 indices via discrete gauging. A class of 4d N=3 SCFTs can be obtained from gauging a discrete subgroup of the global symmetry group of N=4 Super Yang-Mills theory. This discrete subgroup contains elements of both the SU(4) R-symmetry group and the \(SL(2,\mathbb{Z}) \) S-duality group of N=4 SYM. We give a prescription for how to perform the discrete gauging at the level of the superconformal index and Higgs branch Hilbert series. We interpret and match the information encoded in these indices to known results for rank one N=3 theories. Our prescription is easily generalised for the Coloumb branch and the Higgs branch indices of higher rank theories, allowing us to make new predictions for these theories. Most strikingly we find that the Coulomb branches of higher rank theories are generically not-freely generated.

Benjamin Assel

Wilson loops in 5d N=1 theories and S-duality. I will discuss the action of S-duality on half-BPS Wilson loops in 5d N=1 theories. The duality is the statement that different massive deformations of 5d SCFT have different 5d gauge theory descriptions. The pairs of dual theories that I will discuss are realized by IIB brane webs which are S-dual to each other. Using the brane realization of the loop insertions I will explain that Wilson loops are mapped to dual Wilson loops with a specific map of representations. I will also show exact localization computations confirming the string theory predictions.

Wednesday

Mathew Bullimore

Twisted Hilbert Space of 3d Supersymmetric Gauge Theories. I will discuss aspects of 3d supersymmetric gauge theories on the product of a line and a Riemann surface. Performing a topological twist along the Riemann surface leads to an effective supersymmetric quantum mechanics on the line. I will outline a construction of the space of supersymmetric ground states in terms of the cohomology of vortex moduli spaces on the Riemann surface. This exhibits a rich dependence on deformation parameters compatible with the twist, such as mass parameters and background vector bundles associated to flavour symmetries, allowing for more refined tests of 3d mirror symmetry.

Sara Pasquetti

T[SU(N)] duality webs. I will present various new IR dualities between 3d N=2 quiver theories. Some of the 3d theories that I will discuss can be interpreted as codimension-two defect theories coupled to a 5d bulk theory, in this case the 3d duality follows from S-duality for the bulk theory. I will then discuss how these dualities relate to the gauge/q-CFT correspondence connecting 3d N=2 quiver theories to correlators of q-deformed Toda vertex operators and briefly mention the reduction from 3d to 2d.

Matthew Buican

Flowing from 16 to 32 Supercharges. I will explore an infinite set of strongly coupled RG flows starting from certain exotic 4D N=2 SCFTs in the UV and ending up at a set of SCFTs with 32 (Poincare plus special) supercharges in the IR. I will comment on possible implications of this study on the space of theories with 32 supercharges.

Anton Nedelin

T[SU(N)] duality webs II: Gauge/CFT correspondence and 2d limit. In this talk we will continue describing web of dualities for 3d T[SU(N)] theories. We will start by giving short introduction to Dotsenko-Fateev representation of conformal blocks in Toda theory. Then we will discuss q-deformed W algebras as well as corresponding deformation of Toda CFT and its conformal blocks. Finally we will establish correspondence between these q-deformed conformal blocks and holomorphic blocks of 3d theories. In second part of the talk we will discuss in details consequences of 3d mirror symmetry for gauge/CFT correspondence, which includes spectral duality of qCFT conformal blocks and 2d gauge/CFT correspondence obtained from the q→1 limit of 3d web of dualities.

Simone Giacomelli

Three dimensional SQCD and mirror symmetry. In this seminar I will discuss monopole operators in the context of supersymmetric gauge theories in three dimensions. Using then a recently proposed duality for U(N) supersymmetric QCD (SQCD) in three dimensions with monopole superpotential, I will derive the mirror dual description of N=2 SQCD with unitary gauge group, generalizing the known dual description of abelian gauge theories. A variant of this procedure can be used to extract dual descriptions of adjoint SQCD as well. I will propose a duality for adjoint SQCD with two colours and arbitrary number of flavors and discuss the subtleties arising for more general gauge groups.

Luca Cassia

3d dualities and Weyl group symmetry. In this talk I will present various aspects of the 4d/3d reduction of N=1 dualities involving USp(2N) gauge theories with 8 fundamentals and one antisymmetric matter field. I will discuss the non-trivial role played by monopole superpotentials in the reduction and obtain a large number of new 3d dualities for models with both symplectic and unitary gauge groups, generalizing many previously known results. Moreover I will show how this interesting pattern of dualities is related to global symmetry enhancement governed by the structure of the Weyl group of E7 and of its parabolic subgroups.

Vladimir Bashmakov

Phases of N=1 Adjoint SQCD in 2+1 Dimensions.

In this talk I will review a recent proposal regarding the infrared phases of the three-dimensional N=1 vector multiplet, coupled to the matter multiplet in the adjoint representation. 3d N=1 supersymmetry allows for the jumps of Witten index at co-dimension one walls in the parameter space. Also it is not powerful enough to forbid perturbative generation of the superpotential. All these features will play a crucial role in the analysis of the infrared phases.