Penrose Limit: A Stringy Regime in Holography by Minxin Huang

Penrose limit provides a promising avenue to the stringy regime in the AdS/CFT holography, giving rise to the pp-wave background. Recently, we proposed a novel entry of the pp-wave holographic dictionary, which equated the Berenstein-Maldacena-Nastase (BMN) two-point functions in free Yang-Mills theory with the norm squares of the quantum unitary transition amplitudes between the corresponding tensionless strings. If our proposal is correct, it would not only provide first examples of systematic calculations of the higher genus critical superstring amplitudes, but may also in principle gives exact complete results for any string coupling, due to the convergence of genus expansion.

Instanton Counting in BCD-type Gauge Theories and O-vertex by Ruidong Zhu

Localization method together with ADHM construction provide a powerful way to compute the exact partition function of 8 SUSY gauge theories. In particular, Nekrasov’s partition function is interesting because of the non-perturbative corrections from instantons. It is, however, known to be difficult to perform the integrals in an analytic way that appear in the computation of instanton partition functions of BCD-type gauge theories. In this talk, we propose an analytic expression for these integrals in the unrefined limit in the form of summation over Young diagrams. Our results are inspired by the topological vertex formalism in topological string theory.

3d $N=4$ Unitary/Orthosymplectic Duality by Satoshi Nawata

There are two ways to realize 3d $N=4$ $Sp(k)$ SQCDs in Type IIB string theory: either $O3^+$ plane or $O5^-$ plane. The mirror dual to the $O3^+$ plane realization is an orthosymplectic quiver theory whereas the mirror dual to the $O5^-$ plane realization is a unitary quiver theory. Using exact partition functions, we will show that these two mirror theories are dual to each other, and we also reveal brane dynamics with O-plane. Similarly, considering 5d $N=1$ $Sp(k)$ SQCDs at the infinite coupling limit, the magnetic quiver techniques find a pair of 3d $N=4$ unitary and orthosymplectic quiver with the same Higgs and Coulomb branch. We also discuss the duality between these magnetic quivers. I will end the talk with lots of open problems, expecting insightful feedbacks from audiences. This is about ongoing joint work with M. Sperling, Z. Zhong, and H. Wang.

OPE Coefficients of ABJM Theory with Giants (Part I) by Yunfeng Jiang

This is a joint talk with Jun-Bao Wu. In these talks, we will present recent results on the exact computation of giant graviton OPE coefficients in ABJM theory. In part I, we will first introduce the general background and motivations for this series of works. Then we will explain the method of computation at weak coupling, which includes a large $N$ effective field theory and a novel coordinate Bethe ansatz solution for the alternating SU(4) integrable spin chain. The final result of the OPE coefficient takes the form of an overlap between an on-shell Bethe state and an integrable boundary state.

OPE Coefficients of ABJM Theory with Giants (Part II) by Junbao Wu

This is a joint talk with Yunfeng Jiang. In these talks, we will present recent results on the exact computation of giant graviton OPE coefficients in ABJM theory. In part II, we will focus on the holographic computations which is dual to strong coupling in the gauge theory side. Our approach resolves puzzles and confusions in the literature on the holographic computation of correlation functions of heavy operators. In particular, we point out two important effects which are often missed in the literature; the first one is an average over classical configurations of the heavy state, which physically amounts to projecting the state to an eigenstate of quantum numbers. The second one is the contribution from wave functions of the heavy state. To demonstrate the power of the method, we first analyze the three-point functions in $\mathcal{N}=4$ super Yang-Mills and reproduce the results in field theory from holography, including the cases for which the previous holographic computation gives incorrect answers. We then apply it to ABJM theory and make solid predictions at strong coupling.

5d and 6d SCFTs from C3 Orbifolds by Yinan Wang

I’m going to talk about the construction of 5d SCFTs from M-theory on C3 orbifold singularities, which are classified by the discrete subgroups of $SU(3)$. The properties of such 5d SCFTs are studied using two methods: (1) group theoretic data and 3d Mckay correspondence; (2) resolution of the singularity which corresponds to the 5d Coulomb branch. In certain cases, the threefold singularity can also be embedded into an elliptic model, which leads to a 6d $(1,0)$ SCFT in the F-theory framework. We find new rank-1 6d SCFTs without gauge groups.

Closed-form Schur Indices by Yiwen Pan

Schur index is a remarkable observable associated to any 4d $N=2$ SCFT, and plays a central role in the SCFT/VOA correspondence. In this talk, I will discuss an elementary method to compute them in closed-form in terms of finite sum of Eisenstein series. In particular, we derive a compact closed-form formula for all A1-theories of class-S, and conjecture closed-form unflavored indices for $N=4$ theories with $SU(N)$ gauge groups. Some applications will also be discussed.

6d Seiberg-Witten Curves and 5-brane Webs by Sung-Soo Kim

In this talk, we discuss the construction of the Seiberg-Witten (SW) curves based on Type IIB 5-brane webs. After reviewing the construction for SW curves for 5d supersymmetric gauge theories, we discuss how to generalize it to 6d superconformal theories which can be realized on a 5-brane webs with periodic direction. In particular, we construct the SW curve for 6d E-string theory using a 5-brane web with two O5-planes. In fact, the E-string SW curve is already constructed by Eguchi and Sakai which is rather complicated. Our expression is, however, much simpler than the Eguchi and Sakai’s one. We discuss equivalence between our curve and the Eguchi and Sakai. Finally we further generalize our construction of the SW curves to 6d little string theories.

Thermodynamic Limit of Nekrasov Partition Function for 5-brane Web with O5-plane by Futoshi Yagi

We study 5d $N=1$ $Sp(N)$ gauge theory with $Nf\;( \leq 2N + 3 )$ flavors based on 5-brane web diagram with O5-plane. On the one hand, we discuss Seiberg-Witten curve directly from the 5-brane web. In this process, the boundary conditions originated from the O5-plane plays a key role. On the other hand, we compute the Nekrasov partition function based on the topological vertex formalism with O5-plane, which is the generalization for the conventional topological vertex. Rewriting it in terms of profile functions, we obtain the saddle point equation for the profile function after taking thermodynamic limit. By introducing the resolvent, we derive the Seiberg-Witten curve and its boundary conditions as well as its relation to the prepotential in terms of the cycle integrals. They coincide with those directly obtained from the 5-brane web. This result would shed light on the mirror symmetry for non-toric Calabi-Yau 3-folds including D-type singularities, which is expected to be related to the 5-brane web diagram with O5-plane.

Anomalies and Supersymmetry by Ioannis Papadimitriou

I will discuss ‘t Hooft anomalies of continuous global symmetries in supersymmetric quantum field theories, focusing on the structure and role of the fermionic components of such anomalies and how they can be determined using a generalized anomaly descent procedure, or through supersymmetric anomaly inflow. I will then show that the fermionic components of supersymmetric ‘t Hooft anomalies result in a deformation of the charge superalgebra that affects the dependence of supersymmetric observables on the moduli of curved backgrounds admitting Killing spinors. The implications of this observation for precision tests of holographic dualities through supersymmetric localization will also be discussed.

Representations of Quantum W subalgebras by Hong (Kilar) Zhang

We discuss the vertical and horizontal representations of Quantum W subalgebras, and confirm the Awata-Feigin-Shiraishi interwiner lemma which encodes the quantum constraints on the self-dual topological vertex.

Worldsheet Variables for Cluster Configuration Spaces and Hypersurface Arrangements by Peng Zhao

We introduce worldsheet variables for a certain moduli space associated with a Dynkin diagram of finite type. The construction is based on gluing a pair of A-type quivers. We find new nonlinear factors that characterize such spaces as hypersurface arrangement complement. We study various topological properties using a finite-field method and propose conjectures about quasi-polynomial point count, dimensions of cohomology, and Euler characteristics for the $D_n$ space up to $n=10$. These new variables have applications for string integrals, cluster alphabets, etc.

Brane construction of the Bethe/gauge correspondence for superspin chains by Junya Yagi

I will discuss a superalgebra generalization of the Bethe/gauge correspondence between 2d $N=(2,2)$ quiver gauge theories and rational spin chains. I will give a derivation of the correspondence by mapping it to 4d Chern-Simons theory via string dualities. Based on joint work with Nafiz Ishtiaque, Seyed Faroogh Moosavian and Surya Raghavendran.