Title and abstract


--- Mar 22 (Mon) ---

Yasuyuki Hatsuda (Rikkyo U.)
Title: Black Hole Quasinormal Modes and Seiberg-Witten Theory
Abstract: Black hole perturbation theory leads to ordinary differential equations. Typically the resulting equations belong to Heun's differential equation and its confluent cousins. The same equations turn out to be found in a "quantization" of Seiberg-Witten theory. I will explain what we can predict from this relation to black hole physics.


Yutaka Yoshida (Kavli IPMU)
Title: Monopole bubbling and BPS 't Hooft operators in three, four, and five dimensions
Abstract: We evaluate the vacuum expectation values of half-BPS 't Hooft operators in supersymmetric gauge theories with eight supercharges in three, four, and five dimensions in terms of supersymmetric localization.

In localization formulas, there exist non-perturbative contributions from the moduli of Dirac monopoles screened by 't Hooft-Polyakov monopoles, called monopole bubbling effects (a.k.a. monopole screening effects).
By introducing orientifolds, we generalize the brane construction of monopole bubbling effects for SU(N) gauge theories to O(N) and USp(N) gauge theories.


Masahito Yamazaki (Kavli IPMU)
Title: Quiver Yangians


Junya Yagi (Tsinghua U.)
Title: 4d Chern-Simons theory and the Bethe/gauge correspondence for superspin chains
Abstract: I will discuss a string theory perspective on the Bethe/Gauge correspondence for the XXX superspin chain. I explain how to realize 4d Chern-Simons theory with gauge supergroup using branes, and how the brane configurations for the superspin chain get mapped to 2d N = (2,2) quiver gauge theories proposed by Nekrasov. This is based on my ongoing work with Nafiz Ishtiaque, Faroogh Moosavian and Surya Raghavendran.


Masashi Hamanaka (Nagoya U.)
Title: Multi-soliton solutions to Anti-Self-Dual Yang-Mills Equations
Abstract: We construct exact multi-soliton solutions to anti-self-dual Yang-Mills (ASDYM) equations for G=GL(2,C) or G=U(2). The solutions have localized action density on three-dimensional hyperplane (domain-wall type) and are different from instantons. The multi-soliton solutions can be obtained by Darboux transformations and represented by Wronskian-type determinants, which might be fit to Sato's formulation of KP soliton theory. We discuss behavior of them (soliton scatterings, domain-wall reconnections etc.). This is collaboration with Claire Gilson and Jon Nimmo (Glasgow) and Shan-Chi Huang (Nagoya).


Ryo Suzuki (Yau Center, Southeast University)
Title: Oscillating multiple giants
Abstract: In this talk I present a new example of the AdS/CFT correspondence involving multiple D-brands. At weak coupling, we propose an all-loop ansatz which diagonalizes the mixing of the operators in the su(2) sector of N=4 SYM with O(Nc) dimensions. It was expected that these operators are dual to open strings attached to multiple giant gravitons. At strong coupling, however, non-maximal giants can be deformed by an infinitesimal energy. Thus I propose an oscillating D-brane solution as a good candidate for the object corresponding to the all-loop ansatz.

Shamil Shakirov (IITP)
Title: Integrable systems from Chern-Simons TQFT
Abstract: Chern-Simons TQFT associates vector spaces to two-dimensional surfaces and linear operators to bordisms between surfaces. Sometimes for topological reasons these operators commute. We will show how, in certain cases, this leads to a many-body integrable system of Ruijsenaars-Schneider type, and discuss their properties.



--- Mar 23 (Tue) ---

Masazumi Honda (YITP, Kyoto U.)
Title: Quantum phase transition and Resurgence: Lessons from 3d N=4 SQED
Abstract: We study a resurgence structure of a quantum field theory with a phase transition to uncover relations between resurgence and phase transitions. In particular we focus on three-dimensional $\mathcal{N}=4$ supersymmetric quantum electrodynamics (SQED) with multiple hypermultiplets, where a second-order quantum phase transition has been recently proposed in the large-flavor limit. We provide interpretations of the phase transition from the viewpoints of Lefschetz thimbles and resurgence. For this purpose, we study the Lefschetz thimble structure and properties of the large-flavor expansion for the partition function obtained by the supersymmetric localization. We show that the second-order phase transition is understood as a phenomenon where a Stokes and anti-Stokes phenomenon occurs simultaneously. The order of the phase transition is determined by how saddles collide at the critical point. In addition, the phase transition accompanies an infinite number of Stokes phenomena due to the supersymmetry. These features are appropriately mapped to the Borel plane structures as the resurgence theory expects. Given the lessons from the SQED, we provide a more general discussion on the relationship between the resurgence and phase transitions. In particular, we show how the information on the phase transition is decoded from the Borel resummation technique.


Shuichi Yokoyama (YITP, Kyoto U.)
Title: U(1) spin Chern-Simons theory and Arf invariants in 2d
Abstract: It is known that a 3d U(1) Chern-Simons theory is spin if the level is odd. We demonstrate this by casting the dynamics of U(1) Chern-Simons theory into the theory of a 2d compact boson with a certain radius and twisting it incorporating the Arf invariant. We show that the resulting twisted theory is spin and its symmetry is extended so that the torus partition function can be reorganized into a finite sum involving a finite set of the characters for the extended chiral algebra. Employing these characters we compute the modular matrices and the partition function of the corresponding abelian Chern-Simons theory on the lens space L(a,1), which encodes the expected dependence on the 3d spin structure.


Meer Ashwinkumar (Kavli IPMU)
Title: Integrable Lattice Models and Holography
Abstract: We study four-dimensional Chern-Simons theory on D×C (where D is a disk), which is understood to describe rational solutions of the Yang-Baxter equation from the work of Costello, Witten and Yamazaki. We find that the theory is dual to a boundary theory, that is a three-dimensional analogue of the two-dimensional chiral WZW model. This boundary theory gives rise to a current algebra that turns out to be an "analytically-continued" toroidal Lie algebra. In addition, we show how certain bulk correlation functions of two and three Wilson lines can be captured by boundary correlation functions of local operators in the three-dimensional WZW model. In particular, we reproduce the leading and subleading nontrivial contributions to the rational R-matrix purely from the boundary theory.


Hajime Nagoya (Kanazawa U.)
Title: Irregular conformal blocks and Painlevé tau functions
Abstract: The tau function of the sixth Painlevé equation(PVI) is a Fourier transform of the four-point conformal block of the Virasoro algebra with the central charge c=1. It is known that the other Painlevé equations are limits of PVI. I will explain irregular conformal blocks appeared in series representations of Painlevé tau functions.


Rajath Radhakrishnan (Queen Mary U. of London)
Title: Anyon Fusion and the Arad-Herzog Conjecture
Abstract: I will explain how anyon fusion in discrete gauge theories is determined by some basic properties of finite groups like conjugacy classes and irreducible representations. I will then focus on discrete gauge theories based on simple groups, and relate the existence problem of non-abelian anyons fusing to give a unique outcome to the Arad-Herzog conjecture.


Takeshi Oota (Osaka City U.)
Title: Critical points of matrix models, and their connection with the supersymmetric gauge theories
Abstract: Recently, we have studied certain unitary matrix models. In this talk, I will explain their connection with the 4D N=2 supersymmetric gauge theories. In particular, the double scaling limit to critical points of the matrix model corresponds to the limit of the gauge theory to the superconformal fixed points.


Alessandro Tanzini (SISSA)
Title: Surface defects from A to G
Abstract: We discuss surface defects in 4d and 5d supersymmetric gauge theories with 8 supercharges. In 4d, we show that the RG flow in presence of defects generates new recursion relations determining multi-instanton corrections in a self-dual Omega background for all simple groups from A_n to G_2. The uplift to 5d is a discrete flow generated by automorphisms of the associated BPS quiver. We show that for a class of theories, the 4d reduction of these discrete flows displays an intriguing new relation with Argyres-Douglas SCFTs.



--- Mar 24 (Wed) ---


Tomoyuki Arakawa (RIMS, Kyoto U.)
Title: 4D/2D duality and representation theory
Abstract: The 4D/2D duality discovered by Beem et al. constructs representation theoretical objects, such as representations of affine Kac-Moody algebras, as invariants of 4 dimensional superconformal field theories with N = 2 supersymmetry. Furthermore, it reveals a remarkable duality between the representation theoretical objects constructed in this way and the geometric invariants called Higgs branch of the original 4 dimensional theory. In this talk, I will discuss about the 4D/2D duality from a representation theoretical perspective.

Ruidong Zhu (Soochow U.)
Title: Topological vertex for O5-planes
Abstract: We propose an extended form of the topological vertex formalism that applies to (p,q)-brane web with orientifolds, by analyzing the geometric transition of Kim-Yagi’s prescription. A new topological vertex with only one leg is introduced into the formalism for the intersection of (2,1)-brane and the O-plane, and we assign a vertex operator to this intersection point in our proposal. We show the consistency of this extended formalism and discuss its potential future usage in the study of SO(N) gauge theories etc.

Zhihao Duan (KIAS)
Title: ABCDEFG of 5d/6d elliptic genera
Abstract: We study elliptic genera of both 6d (2,0) SCFTs and their twisted compactification to 5d. The elliptic genera can be bootstrapped either from instanton counting and the blowup equations, or from modular properties and the perspective of topological strings. As a possible application, we study their Cardy limit and find universal asymptotic behaviour for all simple Lie algebras.


Dan Xie (Tsinghua U.)
Title: 4d N=2 SCFTs and 2d W algebras
Abstract: I will review a series of recent works relating 4d N=2 SCFTs and 2d W algebras. I will first discuss the known examples and the basic maps of physical quantities. Then I will discuss how to learn interesting properties of 4d theories from 2d theories, and vice versa.


Kazuki Kiyoshige (Osaka City U.)
Title :The Chiral Algebra of Genus Two Class S Theory
Abstract:We construct the chiral algebra (or vertex operator algebra) associated with an $A_{1}$ type class $\mathcal{S}$ theory with a genus two Riemann surface, which we call a genus two theory. The genus two theory has an accidental flavor $U(1)_{f}$ symmetry, which is not classified by the ordinary flavor symmetry structure of class $\mathcal{S}$. We identify a set of generators of the associated chiral algebra by the certain BRST reduction. This BRST reduction corresponds to an exactly marginal gauging in the four-dimensional superconformal field theory. We find that these generators form a closed OPE. The set of generators contains various non-scalar Schur operators, especially a semi-short multiplet other than stress tensor multiplet. We conjecture that the set of generators we find is a complete set of generators. The Schur index of the genus two theory calculated from the four-dimensional Lagrangian description and the vacuum character calculated from the list of generators and null states agree, which supports our conjecture. From our OPE results, we find that an unexpected new global $SU(2)$ symmetry which acts on the genus two chiral algebra. Surprisingly, the symmetry does not have any local flavor current in four-dimensional SCFT. We find that this new $SU(2)$ symmetry strongly constrains the OPEs of the non-scalar Schur operators. We exhibit properties appearing in the two-dimensional chiral algebra and predict new properties for four-dimensional physics. This new $SU(2)$ symmetry might indicate one of the advantages of the 4d SCFT / 2d chiral algebra correspondence. We also show that the S-duality of the genus two theory at the level of the Schur index with flavor fugacity.


Simone Giacomelli (Oxford U.)
Title: Superconformal theories from S-fold geometries
Abstract: The term S-fold denotes F-theory compactifications which involve non-trivial S-duality transformations. In this talk I will discuss 4d N=2 preserving S-folds and the worldvolume theories on D3-branes probing them. They consist of two new infinite series of superconformal theories whose distinction lies in the asymptotic holonomy of the gauge bundle on the 7-brane and are classified by automorphisms of the underlying gauge algebra. These models are connected by an interesting web of RG flows and their Higgs branches provide new examples of instanton moduli spaces.


Yutaka Matsuo (U. of Tokyo)
Title: q-Deformation of Corner Vertex Operator Algebras by Miura Transformation
Abstract: Recently, Gaiotto and Rapcak proposed a generalization of W algebra by considering the symmetry at the corner of the brane intersection (corner vertex operator algebra). The algebra, denoted as YL,M,N , is characterized by three non-negative integers L, M, N. It has a manifest triality automorphism which interchanges L, M, N, and can be obtained as a reduction of W1+∞ algebra with a “pit” in the plane partition representation. Later, Prochazka and Rapcak proposed a representation of YL,M,N in terms of L + N + M free bosons by a generalization of Miura transformation, where they use the fractional power differential operators. In this paper, we derive a q-deformation of the Miura transformation. It gives a free field representation for q-deformed YL,M,N, which is obtained as a reduction of the quantum toroidal algebra. We find that the q-deformed version has a “simpler” structure than the original one because of the Miki duality in the quantum toroidal algebra. For instance, one can find a direct correspondence between the operators obtained by the Miura transformation and those of the quantum toroidal algebra. Furthermore, we can show that the both algebras share the same screening operators.



--- Mar 25 (Thu) ---

Nobuyoshi Ohta (Kindai U.)
Title: Asymptotic Safety Approach to Quantum Gravity
Abstract: We review the approach based on the asymptotic safety to the quantum gravity, including the current status and various aspects of the approach. We then discuss our work on the dimension of critical surface, which is one of the important problems in this subject.

Kazuhiro Sakai (Meiji Gakuin U.)
Title: Multi-boundary correlators in 2d topological gravity
Abstract: Jackiw-Teitelboim (JT) gravity is a simple model of 2d gravity to study various issues in quantum gravity and holography. We point out that JT gravity is a special case of traditional 2d topological gravity. This enables us to study JT gravity using powerful techniques developed for topological gravity and matrix models. I will explain how multi-boundary correlators as well as the thermal partition function are computed in JT and general topological gravities by directly solving the KdV equation.


S.N.Hazel Mak (Brown U.)
Title: On 1D, N = 4 Supersymmetric SYK Models
Abstract: Proposals are made to describe 1D, N = 4 supersymmetrical systems that extend SYK models by compactifying from 4D, N = 1 supersymmetric Lagrangians involving chiral, vector, and tensor supermultiplets. Quartic fermionic vertices are generated via integrals over the whole superspace, while 2(q-1)-point fermionic vertices are generated via superpotentials. The coupling constants in the superfield Lagrangians are arbitrary, and can be chosen to be Gaussian random. In that case, these 1D, N = 4 supersymmetric SYK models would exhibit Wishart-Laguerre randomness, which share the same feature among other 1D supersymmetric SYK models in literature. One difference with 1D, N = 1 and N = 2 models though, is our models contain dynamical bosons, but other existing 1D, N = 4 and 2D, N = 2 models also exhibit this property.


Tsunehide Kuroki (Toyota Technological Institute)
Title: Replica wormholes and defects in JT gravity from Liouville theory
Abstract: We consider replica wormholes and defects in JT gravity in terms of boundary Liouville theory. We first make precise connection between the JT gravity and semiclassical Liouville theory. In particular, we clarify how nontrivial physics associated with dilaton in the former is encoded into the latter. According to this dictionary, we can reproduce the precise form of contribution from the replica wormhole to the generalized entropy by applying the replica trick directly to the Liouville theory. Here it is remarkable that even the contribution from the boundary dilaton can be also exactly retrieved. Our dictionary also enables us to identify defects in the JT gravity as the deformation of the Liouville action.


Reiji Yoshioka (OCAMI)
Title: Cut & Join and Op/FD/dessin correspondence


Joseph Ben Geloun (LIPN, Univ Sorbonne Paris Nord)
Title: A lattice interpretation of the Kronecker coefficient from ribbon graph quantum mechanics
Abstract: The action of subgroups on a product of symmetric groups allows one to enumerate different families of graphs. We will focus on bipartite ribbon graphs with at most n edges that we could enumerate as the number of orbits of the adjoint action on two copies of the symmetric group S_n. These graphs form a basis of an algebra which endowed with a certain sesquilinear form becomes an a Hilbert space. Acting on this Hilbert space, we define Hermitians operators that we can interpret as Hamiltonians: we are therefore in the presence of a quantum mechanical model. We show that the multiplicities of the eigenvalues of these operators are precisely the Kronecker coefficients, well-known in representation theory. It is proved that there exists an algorithm that delivers the Kronecker coefficients and allow us to interpret those as the dimension of a sub-lattice of the lattice of the ribbon graphs. Thus, this provides an answer to Murnaghan’s question (Amer. J. Math, 1938) on the combinatorial interpretation of the Kronecker coefficient.


Sanjaye Ramgoolam (Queen Mary U. of London)
Title: Permutation Invariant Gaussian Matrix Models


Hikaru Kawai (Kyoto U.)
Title: Random geometry and naturalness