Title and abstract
Shoto Aoki - Chiral fermion on curved domain-wall
Abstract: We consider a massive fermion system having a curved domain-wall embedded in a square lattice. In a similar way to the conventional flat domain-wall fermion, chiral massless modes appear at the domain-wall but these modes feel "gravity" through the induced spin connections.
Jinbeom Bae - Towards a Classification of Fermionic Rational Conformal Field Theories (slides)
Abstract: A fermionic CFT refers to a conformal field theory with primaries of half-integer spin and entails the spin structures. The torus partition functions of each spin structure are associated with the level-two congruence subgroups such as \Gamma_\theta, \Gamma^{0}(2) and \Gamma_0(2). To explore the landscape of the fermionic RCFTs, we develop the Modular Linear Differential Equations (MLDE) for the level-two congruence subgroups. We show that the partition functions of the fermionic RCFTs are mapped to that of the bosonic RCFTs, such as the WZW models, via the generalized Jordan-Wigner transformation. Furthermore, we propose the necessary conditions for promoting fermionic RCFTs to the supersymmetric RCFTs and discuss the emergent supersymmetry on the edge modes.
Lakshya Bhardwaj - Generalized Symmetries and Anomalies in 3d with Applications to N=4 SCFTs (slides)
Abstract: I will discuss generalized symmetries (1-form, 0-form and 2-group) of 3d gauge theories, along with their ‘t Hooft anomalies. Applying this to “good” 3d N=4 gauge theories lets us also determine the generalized symmetries and anomalies involving enhanced Coulomb branch 0-form symmetries in the IR 3d N=4 SCFTs. The information about these symmetries and anomalies allows us to determine the precise global forms of 3d mirrors/magnetic quivers of 4d Class S theories and 5d SCFTs. The global form of 0-form symmetry groups predicted by these magnetic quivers matches results obtained via other methods in 4d and 5d.
Giulio Bonelli - Spinning Black Holes, 2D CFTs, N = 2 supersymmetric gauge theories & Heun functions (slides)
Abstract: The study of perturbation theory around the Kerr black hole is a classical problem in General Relativity. Due to the high order of symmetry of the gravitational field and the consequent separation of variables at the linear order, the problem reduces to the study of linear ordinary second order differential equations. The resulting equations are of Fuchsian type and therefore, as already observed long ago by A.M.Polyakov, can be solved exactly in terms of classical irregular Virasoro conformal blocks. By making use of the specific exact expressions of the latter implied by the AGT dual perspective on the conformal field theory, it is possible to explicitly solve the connection problem of the resulting (confluent) Heun equation and give novel exact and explicit formulas for the grey body factor, quasi-normal modes and Love numbers of the Kerr black hole.
Abstract: We construct large N saddle points of the matrix model for the N=4 Yang-Mills index dual to the BPS black holes in AdS5 X S5. We find novel solutions given by areal eigenvalue distributions after slightly reformulating the saddle point problem. We also construct a class of multi-cut saddle points, showing that they sometimes admit nontrivial filling fractions. As a byproduct, we find that the Bethe ansatz equation emerges from our saddle point equation.
Zhihao Duan - Resurgence of complex Chern-Simons theory at higher levels (slides)
Abstract: Three-dimensional complex Chern-Simons theory is deeply related to quantum topology of three manifolds and knot theory. In particular, the perturbative expansion of its partition function gives rise to factorially divergent series, which exhibits interesting resurgent structure and provides new insights into 3D-3D correspondence. In my talk, I will discuss resurgent properties of the partition functions on some hyperbolic manifolds at a generic level k, extending previous works on the level k = 1 case. This is based on an upcoming work with Jie Gu.
Dongmin Gang - Exceptional Dehn fillings in 3D-3D correspondence (slides)
Abstract: According to Thurston's Hyperbolic Dehn filling Theorem, Dehn fillings of a 1-cusped hyperbolic 3-manifold are always hyperbolic except for only finitely many exceptional cases. In 3D-3D correspondence, Dehn filling corresponds to gauging of su(2) symmetry and the exceptional Dehn fillings correspond to gauging with small CS levels. Various interesting non-perturbative IR phenomena (such as spontaneous SUSY breaking, generation of mass gap, SUSY enhancement, etc) can emerge under the 'exceptional' gauging. In this talk, I will propose a systematic way of reading off the IR phases of class R theory associated with non-hyperbolic 3-manifold M from basic topological properties of the 3-manifold.
Abhijit Gadde - A scattering amplitude for massive particles in AdS
Abstract: What is the local bulk observable that a dual conformal field theory correlator computes? In the so-called flat space limit, it is the flat space S-matrix. But away from this limit, we don't have a clear answer to this question. In this talk, I will define an observable, called the AdS S-matrix, that is computed using local bulk effective field theory that has the property that it reduces to the flat space S-matrix in the large radius limit. I will describe how to conveniently calculate it using Feynman-like rules and relate it to a more conventional CFT observable namely the Mellin amplitude.
Philip Glass - Cheshire cat resurgence in quantum field theories
Abstract: The resurgence program aims to deepen our understanding of quantum systems such as string theories and quantum field theories by writing observables in these systems as ambiguity-free Borel-Ecalle resummations of transseries. Many interesting features of resurgence theory, such as Stokes phenomena, rely on the existence of a divergent, asymptotic perturbative expansion of an observable. I will discuss how these features manifest in certain examples where the perturbative series is in fact convergent.
Sergei Gukov - Fermionic characters, knots, and BPS quivers (slides)
Amihay Hanany - Hasse diagrams and Quiver Gauge Theories (slides)
Abstract: The moduli space of Supersymmetric gauge theories with 8 supercharges has a rich structure of symplectic singularities associated with degenerations in which additional massless states arise. These are neatly arranged into phase diagrams that encode different the sets of massless states, with information on the moduli that are needed to be tuned in order to move from one phase to another. We will present results from studies of families of quivers, including those on the affine grassmanian of finite dimensional Lie algebras.
Yosuke Imamura - Finite N superconformal index via the AdS/CFT correspondence (slides)
Abstract: I will present a prescription to calculate the superconformal index of the N=4 U(N) supersymmetric Yang-Mills theory with finite N on the AdS side. The finite N corrections are included as contributions of D3-branes wrapped around three-cycles in S5, which are calculated as the index of the gauge theories realized on the wrapped branes. I will also comment on applications to other theories.
Katsushi Ito - ODE/IM correspondence and WKB periods (slides)
Abstract: In this talk I will discuss the ODE/IM correspondence for the linear problem associated with the affine Toda field equations for affine Lie algebras. In particular, we study the (r+1)-th order ODE with polynomial potential. The ODE/IM correspondence provides a relation between the Wronskians of the solutions and the Y-functions which satisfy the thermodynamic Bethe ansatz (TBA) equation. We show the equivalence between the logarithm of the Y-functions and the WKB periods, which is confirmed by solving the TBA equation numerically. We also discuss the wall-crossing of the TBA equations from the minimal chamber to the maximal chamber.
Abstract: We describe joint work with K. Iwaki relating computations in the theory of topological recursion (TR) to Gaiotto-Moore-Neitzke's counting of BPS states in 4d N=2 class S theories, in the case where the latter structure is "uncoupled". In particular, we describe a simple formula expressing the TR free energies as a sum over BPS states for the relevant quadratic differential. We will explain how this picture ought to generalize, and if time permits, the relation to so-called "quantum curves".
Si Li - Elliptic chiral homology and quantum master equation (slides)
Abstract: We present an effective BV quantization theory for chiral deformation of two dimensional conformal field theories. We explain a connection between the quantum master equation and the chiral homology for vertex operator algebras. As an application, we construct correlation functions of the curved beta-gamma/b-c system and establish a coupled equation relating to chiral homology groups of chiral differential operators. This can be viewed as the vertex algebra analogue of the trace map in algebraic index theory. The talk is based on the recent work arXiv:2112.14572 [math.QA].
Sanefumi Moriyama - Duality Cascades and Affine Weyl Groups
Sunil Mukhi - Poincare Series, 3d Gravity and Averages of Rational CFT (slides)
Abstract: I will survey the Poincaré series approach to computing 3d gravity partition functions dual to Rational CFT. For a single genus-1 boundary, the SU(2) WZW models provide unitary examples for which this series is a positive linear combination of two modular-invariant partition functions. This supports the interpretation that the bulk gravity theory - topological Chern-Simons - is dual to an average over CFT’s sharing the same Kac-Moody algebra. I will discuss the generalisation to SU(N) at level 1, where one finds averages over arbitrarily many boundary CFT's.
Emily Nardoni - Confinement in Adjoint QCD from Seiberg Witten Geometry
Abstract: Standard lore suggests that four-dimensional SU(N) gauge theory with 2 massless adjoint Weyl fermions ("adjoint QCD") flows to a phase with confinement and chiral symmetry breaking. In this talk, we will test and present new evidence for this lore. Our strategy involves realizing adjoint QCD in the deep IR of a renormalization group flow descending from SU(N) Seiberg-Witten theory, deformed by a soft supersymmetry-breaking mass for its adjoint scalars. A crucial role in the analysis is played by a dual Lagrangian that originates from the multi-monopole points of Seiberg-Witten theory, and which can be used to explore the phase diagram as a function of the supersymmetry-breaking mass.
Takahiro Nishinaka - The Nekrasov partition function and Schur index of gauged Argyres-Douglas theories
Abstract: We study the Nekrasov partition function (in the classical limit) and Schur index of two 4D N=2 conformal SU(2) gauge theories coupled to Argyres-Douglas (AD) theories, and show that these quantities are obtained, by a simple change of variables, from the same quantities of the SU(2) gauge theory with four fundamental flavors. This change of variables maps “q" to "q^2" or "q^3", where “q" is the exponential of the UV gauge coupling for the Nekrasov partition function while it is the superconformal fugacity for the Schur index. Using this relation, we can particularly read off how the S-duality acts on the UV gauge coupling of these gauged AD theories.
Natalie Paquette - Symmetries, universal defects, and holography (slides)
Abstract: "In this talk, we discuss and characterize certain line and surface defects in supersymmetric quantum field theory and string theory. In particular, we study the constraints arising from gauge or BRST invariance on admissible defects. This point of view has a mathematical translation in terms of a subject called Koszul duality, and its generalizations, which we will explain. We also discuss applications of our Koszul duality point of view for holography: both celestial holography and AdS/CFT. We will show that this point of view provides an expedient way to derive universal symmetry algebras in (holographic) systems. This is based on various works in collaboration with Kevin Costello, and with Brian Williams."
Rajath Radhakrishnan - Quantum codes from conformal field theory (slides)
Abstract: I will describe an explicit map relating rational conformal field theories (RCFTs) and associated bulk Chern-Simons theories to quantum stabilizer codes. Using this map, I will show that point operators in an RCFT correspond to the stabilizer group of the associated quantum code. 0-form symmetries of an RCFT are implemented by topological line operators. I will show that the point operators living at the end of these topological line operators correspond to general elements of the Pauli group. This correspondence leads to a description of orbifolding at the level of the quantum code.
Shu-Heng Shao - Non-invertible Symmetries in Higher Dimensions (slides)
Marcus Sperling - Magnetic quivers and line defects (slides)
Abstract: Supersymmetric Sp(k) quantum chromodynamics with 8 supercharges in space-time dimensions 3 to 6 can be realised by two different Type II brane configurations in the presence of orientifolds. Consequently, two types of magnetic quivers describe the Higgs branch of the Sp(k) SQCD theory. This is a salient example of a general phenomenon: a given hyper-Kahler Higgs branch may admit several magnetic quiver constructions. It is then natural to wonder if these different magnetic quivers, which are described by 3d N = 4 theories, are dual theories. In this talk, I discuss how the unitary and orthosymplectic magnetic quiver theories are subjected to a variety of tests, providing evidence that they are IR dual to each other. For this, sphere partition function and supersymmetric indices are compared. Also, I will introduce half BPS line defects and find interesting regularities from the viewpoints of exact results, brane configurations, and 1-form symmetry.
Kaiwen Sun - Twisted Elliptic Genera (slides)
Abstract: The elliptic genera of 2d (0,4) SCFTs associated to the BPS strings in 6d (1,0) SCFTs have been extensively studied in the past decade. Some special 6d SCFTs allow twisted circle compactification, for example when the gauge algebra admits an outer automorphism. In such cases, the elliptic genera can be generalized to twisted elliptic genera which have many extraordinary properties. We systematically study the twisted elliptic genera including their localization, Higgsing, modular bootstrap, spectral flow symmetry and twisted elliptic blowup equations. Geometrically, they are related to the topological string partition function on genus-one fibered Calabi-Yau threefolds. This is based on a joint work with Kimyeong Lee and Xin Wang.
Yuji Tachikawa - On a rarely-mentioned class of 3d N=4 superconformal field theories (slides)
Abstract: After giving an overview of known highly-supersymmetric conformal field theories in three dimensions, I would like to introduce a class of 3d N=3 superconformal field theories which exhibit supersymmetry enhancement to N=4 when certain strange numerical conditions on the Chern-Simons levels are met. I also discuss if this enhancement can be understood in the context of the 3d/3d correspondence. The talk is based on an unfinished project going back at least five years, in collaboration with Jenny Wong, Benjamin Assel, Alessandro Tomasiello, and Seyed Morteza Hosseini.
Philsang Yoo - Derived Geometry for Physicists (slides)
Abstract: In this largely expository talk, I aim to explain basic ideas of derived geometry and discuss how they are useful in uncovering a new relationship between geometric representation theory and quantum field theory. The original perspective is based on a joint work with Chris Elliott.
Gabi Zafrir - Exceptional moduli spaces for exceptional N=3 theories (slides)
Abstract: It is expected on general grounds that the moduli space of 4d N = 3 theories is an orbifold of flat space by a special type of groups known as crystallographic complex reflection groups (CCRG). For the case of 4d N = 4 theories these further reduce to the Weyl groups of simple Lie algebras. As in the case of Lie algebras, the space of CCRGs consists of several infinite families, together with some exceptionals. To date, no 4d N = 3 theory with moduli space labeled by an exceptional CCRG (excluding Weyl groups) has been identified. In this talk, I shall discuss how one can identify 4d theories realizing such moduli spaces and study some of their properties.
Yunqin Zheng - Symmetry Protected Topological Criticality (slides)
Abstract: Symmetry protected topological (SPT) phases have been extensively studied over the past decade. They are systems with a uniquely gapped symmetric ground state but are not able to be connected to a trivially gapped systems under symmetric local unitary transformation. In this talk, I will show that the notion of SPT for gapped systems can be generalized to critical systems, which we denote as symmetry protected topological criticality (SPTC). I present a general way of constructing topologically nontrivial SPTCs, study their physical observables that characterize the nontrivial topological properties, and study the stability under perturbation. (This talk is based on work in collaboration with Linhao Li (ISSP) and Masaki Oshikawa (ISSP, IPMU). )