Slides are available at this link: slides
Kimyeong Lee
Title: On 5d Super Conformal Field Theories
Abstract: In this talk, I review some salient aspects of the 5d SCFTs and speculate its future directions. Especially, I focus on the subjects I have worked on.
Yunfeng Jiang
Title: Integrability breaking and soliton confinement
Abstract: Integrability is interesting, often associated with remarkable phenomena such as the existence of infinitely many conserved charges, factorized scattering and exact solvability. On the other hand, it is probably even more interesting to break integrability, giving rise to new phenomena such as particle production, resonance states, and notably, soliton confinements. In this talk, I will first review confinement in Ising field theory and the theoretical works to determine the associated meson spectrum. I will then present recent work in which we explore analogous phenomena in an Ising ladder system. In this setting, we observe similar confinement mechanisms but encounter a richer meson spectrum, including both interchain and intrachain mesons. I will discuss the methods used to determine these spectra and present the key findings of our study.
Yinan Wang
Title: 3d N=2 field theory from M-theory on CY4
Abstract: In this talk I will present our recent developments of constructing 3d N=2 SUSY field theories from M-theory on local CY4 singularities. I will establish the geometric/physics dictionary and present our recent work on a new geometric transition of CY4, leading to confinement in 3d N=2 theories. References: 2312.17082, 2501.07116.
Shi Cheng
Title: 3d theories labeled by branched covers
Abstract: We focus on 3d theories T[M_3] that are given by M5-branes wrapping on closed three-manifolds M_3. For example, abelian 3d theories are determined by plumbed three-manifolds. Various properties of three-manifolds, such as Kirby moves and their generalized versions, have interpretations in terms of 3d theories. Thus, Dehn surgeries play an important role. In this talk, we present a more promising method, which represents closed three-manifolds as branched covers over knots. The key idea is the foliation of three-manifolds, and each slice is a Riemann surface. This realizes the 3d theories as the domain walls of 4d class-S theories. Here, these knots are the branched loci. Surprisingly, there is a dictionary between Dehn surgery and branch cover, which allows us to read off the 3d theories from knots.
Tomoki Nosaka
Title: New recursion relation for M2-brane matrix models
Abstract: A 3d SUSY gauge theory whose S^3 free energy scales as N^{3/2} for large rank N of the gauge group can be a theory on N M2-branes and dual to M-theory on an AdS4 background. For some special setups we can show, by the technique called Fermi gas formalism, that the all order 1/N corrections are given by the expansion coefficients of the Airy function. This stimulated the analysis of the quantum corrections in the gravity side, where it is suggested that the Airy function is a universal structure for all theories of M2-branes. However, in the setups without Fermi gas formalism, currently there are no techniques available to obtain the all order 1/N corrections. In this talk we focus on the finite N exact values of the partition functions and argue their recursion relations with respect to N, which may offer a new tool to study the large N expansion.
Jin Chen
Title: Super-strip Algebra in Gaped Fermionic Models
Abstract: In this talk, I will discuss generalized symmetreis in two-dimensional gaped fermionic systems. In the phase where the symmetric category of the theory is spontaneously broken, we establish a structure, dubbed by super-strip algebra, to describe how the generalized symmetries interpolate different Hilbert spaces defined by vacua in the gaped model.
Xin Gao
Title: Orientifold Calabi-Yau threefolds: Construction and Machine Learning
Abstract: Using the Kreuzer-Skarke database of 4-dimensional reflexive polytopes, we systematically constructed a new database of orientifold Calabi-Yau threefolds up to h^{1,1}(X) = 12. Our approach involved a non-trivial Z_2 involution, with both divisor exchanging and multi-reflections, acting on the Calabi-Yau manifolds. Each of such proper involutions will result in an orientifold Calabi-Yau manifolds and 320,386,067 of them was constructed. We developed a novel algorithm that significantly reduces the complexity of determining the fixed locus under the involutions, followed by the locations of different types of O-planes. It shows that under the proper involutions one end up with majority the O3/O7-planes system and most of them will further admit a naive Type IIB string vacua. Additionally, a new type of free action was determined. We also computed the smoothness and the splitting of Hodge numbers for these orientifold Calabi-Yau threefolds. Finally, We use Graphic machine learning technique together with transformer structure to predict the polytope which can result in an orientifold Calabi-Yau hypersurface and the “naive type IIB string vacua.”
Ban Lin
Title: Categorical aspects of monodromies of Calabi-Yau 3-fold flops
Abstract: The monodromies of B-brane central charges of a CY3 X on its stringy Kahler moduli space M_K(X) can be understood as the auto-equivalences of the derived category of coherent sheaves, B, on X. When X is realized as the target of a geometric phase of a 2d (2,2) GLSM, the grade restriction rule from hemisphere partition function, and hence the window category it defines, computes such monodromy action as window shift monodromy M(B). We elaborated the application of the abelian grade restriction rule in the Herbst, Hori, Pages paper on a large class of X in the type I flop CICY configurations, and concluded that M(B)=TP_ N(B(-P)) with TP_N a simple action of N contracted curves under the flop. It’s proposed that M(B) should depend on the pi_1(M_K(X)) and can be given by the braided action of the spherical twists of O_X and others. This is discussed on some examples. Based on a joint work with Mauricio Romo.
Satoshi Nawata
Title: DAHA, MTC, AD-theory
Abstract: Certain finite-dimensional representations of DAHA receive PSL(2,Z) action. This modular action can be categorized by the modular tensor categories of VOA, associated to Argyres-Douglas theories. In fact, there is a bijection between a fixed-point sets of the Coulomb branch of the AD theories under the U(1)-action, and the Grothendieck group of MTC. This talk is based on the joint work [arXiv:2206.03565] with Gukov-Koroteev-Pei-Saberi, plus recent developments.
Tim Sulimov
Title: BV Amplitudes
Abstract: I will discuss a novel approach to deriving symmetries of amplitudes from symmetries of the action. It has two main features: firstly, it allows one to treat nonlinear symmetries which do not preserve the quadratic part of the action; secondly, it naturally includes on-shell symmetries. The approach makes use of Batalin-Vilkovisky formalism, which will be explained in sufficient detail. I will illustrate all the procedures with informative but easy to follow examples.
Jiahua Tian
Title: What does symmetry say
Abstract: In this talk I will derive the action of a topological field theory in the bulk whose quantization leads to wave functionals that captures flavor symmetries of the QFT on the boundary. The 't Hooft anomaly of a flavor G-symmetry is shown to be characterized by the corresponding Lie algebra cohomology, which, via certain mathematical facts, dictates the necessity of rooting the anomaly into one-higher dimension. The talk is based on 2503.04546 and upcoming works of the same collaboration.
Sung-Soo Kim
Title: Orientifolds, Freezing, and New vertex formalism
Abstract: In this talk, we present a novel perspective on orientifold planes in Type IIB string theory, providing a new tool for engineering supersymmetric gauge theories with SO or Sp gauge groups, as well as certain non-Lagrangian theories. Specifically, we introduce a mechanism—referred to as "the freezing"—for obtaining positively charged orientifolds (O7^+) by placing a particular set of D-branes at the position of an O7^- plane. Building on this approach, we propose a new vertex associated with the O7^+ plane, which facilitates the computation of partition functions for supersymmetric gauge theories whose brane configurations involve an O7^+. Notable examples include SO(N) and SU(N) gauge groups with symmetric matter representations.
Jie Gu
Title: Resurgent structure of 2d Yang-Mills theory on a torus
Abstract: We study the resurgent structure of the topological string dual to 2d U(N) Yang-Mills on torus. We find closed form formulas for instanton amplitudes up to arbitrarily high instanton orders, based on which we propose the non-perturbative partition function including contributions from all the real instantons, and it is uniqe and real for positive modulus and string coupling. We also explore complex instantons and find two infinite towers of them. We expect them to correpond to BPS states in type II string.
Hongliang Jiang
Title: AdS_3 × S^3 Virasoro–Shapiro amplitude with KK modes
Abstract: Generalizing string amplitudes beyond flat spacetime is a central and challenging problem. We address this by computing the first curvature correction to the string amplitude of four Kaluza–Klein (KK) modes on AdS_3 × S^3 × M_4, with M_4 = K3 or T^4, in type IIB string theory. This is holographically dual to the four–point correlator <O_{p_1} O_{p_2} O_{p_3} O_{p_4}> of certain half–BPS operators in the boundary D1–D5 CFT. The result takes the form of an integral over the Riemann sphere, analogous to the flat–space Virasoro–Shapiro amplitude, but with insertions of single–valued multiple polylogarithms of weight three. Our results are obtained in two steps. First, we derive the AdS_3 x S^3 Virasoro–Shapiro amplitude in the special case <O_p O_p O_1 O_1>, by matching the CFT block expansion with an ansatz based on single–valued multiple polylogarithms. We then employ the AdS_3 × S_3 Mellin formalism to generalize the result to the general case of four arbitrary KK modes <O_{p_1} O_{p_2} O_{p_3} O_{p_4}>. Our analysis yields an infinite set of results for operator anomalous dimensions and OPE data in D1–D5 CFT at strong coupling.
Hongfei Shu
Title: Wall-crossing and TBA equations for deformed supersymmetric quantum mechanics
Abstract: The TBA/WKB correspondence describes a mysterious correspondence between the TBA equations of the quantum integrable model and the exact WKB method of the Schroedinger equation. In this talk, we will first provide an overview on the TBA/WKB correspondence, and then apply this framework to the Schroedinger equation for deformed supersymmetric quantum mechanics. The TBA equations and the corresponding wall-crossing will be shown.
Peter Koroteev
Title & Abstract: TBA
Yehao Zhou
Title: Stable envelope for critical loci
Abstract: In this talk we will introduce a generalization of Maulik-Okounkov’s stable envelopes to equivariant critical cohomology. In the case of a tripled quiver variety with standard cubic potential, this reduces to MO’s stable envelope for the Nakajima variety of the corresponding doubled quiver along the dimensional reduction. We define non-abelian stable envelopes for quivers with potentials following a similar construction of Aganagic-Okounkov, and use them to relate critical COHAs to the abelian stable envelopes. RTT formalism leads to natural (shifted) (super) Yangian action on the critical cohomology of quiver varieties with potentials. This talk is based on joint work with Yalong Cao, Andrei Okounkov, and Zijun Zhou.
Kaiwen Sun
Title: Nahm sums and 2d CFTs
Abstract: Nahm sums, also called fermionic sums are some special q-series which are closely related to the characters of 2d CFTs and SCFTs. For example, the renowned Rogers-Ramanujan functions are Nahm sums and also the characters of Lee-Yang model M(5,2). It is an open question to classify the Nahm sums with modularity. I will discuss some recent progress on Nahm sums and generalized Nahm sums, and their connection with 2d CFTs.
Wei Cui
Title: Non-Invertible Surface Defects in 2+1d QFTs from Half Spacetime Gauging
Abstract: We study duality defects in 2+1d theories with $\bZ^{(0)}_N\times\bZ^{(1)}_N$ global symmetry and trivial mixed 't Hooft anomaly. By gauging these symmetries simultaneously in half of the spacetime, we define duality defects for theories that are self-dual under gauging. We calculate the fusion rules involving duality defects and show that they obey a fusion 2-category. We also construct the corresponding symmetry topological field theory, obtained from a four-dimensional BF theory gauging a $\mathbb{Z}_4^\text{EM}$ electric-magnetic symmetry. Furthermore, we provide explicit examples of such duality defects in $U(1)\times U(1)$ gauge theories and in more general product theories. Finally, we find duality defects in non-Lagrangian theories obtained by compactification of 6d $\cN=(2,0)$ SCFTs of type $A_{N-1}$ on various three-manifolds.
Mykola Dedushenko
Title & Abstract: TBA
Xin Wang
Title: Refined BPS numbers on compact Calabi-Yau threefolds from Wilson loops
Abstract: We relate the counting of refined BPS numbers on compact elliptically fibred Calabi-Yau threefolds $X$ to Wilson loop expectation values in the gauge theories that emerge in various rigid local limits of the 5d supergravity theory defined by M-theory compactification on $X$. In these local limits $X_*$, the volumes of curves in certain classes go to infinity, the corresponding very massive M2-brane states can be treated as Wilson loop particles and the refined topological string partition function on $X$ becomes a sum of terms proportional to associated refined Wilson loop expectation values. The resulting ansatz for the complete refined topological partition function on $X$ is written in terms of the proportionality coefficients which depend only on the $\epsilon$ deformations and the Wilson loop expectation values which satisfy holomorphic anomaly equations. Since the ansatz is quite restrictive and can be further constrained by the one-form symmetries and 6d SCFT limits for large base curves, we can efficiently evaluate the refined BPS numbers on $X$, which we do explicitly for local gauge groups up to rank three and $h_{11}(X)=5$. These refined BPS numbers pass an impressive number of consistency checks imposed by the direct counting of these numbers using the moduli space of one-dimensional stable sheaves on $X$ and give us numerical predictions for the complex structure dependency of the refined BPS numbers.
Wei Gu
Title: On mixed ’t Hooft anomalies of emergent symmetries
Abstract: There is an important question: can we probe the UV dynamics from given IR data by utilizing the 't Hooft anomaly? We demonstrate that, under certain conditions, the UV theory must contain non-genuine operators. Our primary examples illustrating this phenomenon are 2D gauged linear sigma models and 3D ChernSimons-matter theories. Through this analysis, we establish connections between different classes of topological quantum field theories and propose a correspondence between quantum cohomologies of distinct target spaces.
Yiwen Pan
Title: Chiral algebra modules of a=c theories
Abstract: Every 4d $\mathcal{N} = 2$ SCFT is associated to a chiral algebra, whose modules are expected to encode BPS non-local operators in 4d. In this talk we will discuss the modules of the chiral algebras associated to the 4d $\mathcal{N} = 4$ $SU(N)$ theories and the TpN theories that satisfy central charge relation $a = c$. We will present the candidate of all the characters of the $\mathcal{N} = 4$ chiral algebras by analyzing Wilson line index. We support our claim by looking at spectral flow of the vacuum module, their relation with the modules associated to the TpN chiral algebras, and 4d mirror symmetry.
Arkadij Bojko
Title: Deformations of vertex algebras from wall-crossing
Abstract: To prove important conjectures for sheaf-counting invariants on Calabi-Yau fourfolds, I introduce additive deformations of vertex algebras. They appear by twisting Joyce’s wall-crossing framework by tautological insertions. After presenting the axioms and their motivation, I will address a particular conjecture by relying on this theory. Under additional assumptions, this proves a DT/PT correspondence for Fano 3-folds.
Leonardo Santilli
Title: SymTFTs and (-1)-form symmetry from M-theory
Abstract: (For Physicists) I will show how the formalism of gerbes encompasses all notions of invertible symmetries, including (-1)-form symmetries. After this general introduction and motivation, I will use differential cohomology to obtain the SymTFT of M-theory compactifications. In this way, I will provide a comprehensive treatment of defects and symmetries via geometric engineering, and derive the (-1)-form symmetries and their anomalies from this perspective. I will conclude with explicit examples and dynamical applications.
(For Mathematicians) I will study the differential cohomology of the Milnor fibre of singular manifolds with special holonomy, of dimension up to 7. I will explain the physical meaning and implications of the perfect pairing between differential cohomology/homology.
Based on joint work with M. Najjar and Y.-N. Wang [2411.19683]
Xinyu Zhang
Title: Physical approach to K-theoretic Donaldson invariants
Abstract: A cornerstone of modern mathematical physics is the deep relation between geometric structures and gauge theory. After briefly reviewing some basic aspects of Donaldson-Witten theory, we will sketch a systematic physical approach to its K-theoretic generalization. This advancement is achieved through the path integral of 5d N=1 SU(2) super Yang-Mills theory defined on $X \times S^1$, where $X$ is a closed, smooth four-manifold. After a partial topological twist along $X$, the correlation functions produce K-theoretic Donaldson invariants. We then evaluate the K-theoretic Donaldson invariants using both UV and IR approaches.
Vyacheslav Lysov
Title: Tropical mirror symmetry via topological quantum mechanics
Abstract: I will describe the Landau-Ginzburg-Saito theory for mirror superpotentials and define n-point correlation functions of Jacobi ring observables. The definition of higher point correlation functions requires additional data: K. Saito's good section, the choice of special representatives in Jacobi ring classes. I will construct the tropical good section from the tropical mirror symmetry.I will introduce tropical curves and define Gromov-Witten invariants. I will formulate the higher topological quantum mechanics (HTQM) on trees and show that its amplitudes describe tropical GW invariants. The mirror symmetry is a resummation of the amplitudes in HTQM into amplitudes in HTQM, deformed by the superpotential. The superpotential is the usual mirror superpotential for the toric mirror. I will demonstrate that the deformation of the evaluation states corresponds to the tropical good section.
Rui-Dong Zhu
Title: Variational Quantum Algorithms for Spin Models
Abstract: The variational quantum algorithm is an optimization method inspired by the quantum computing, and it can naturally be applied to quantum spin chains. In the first half of this talk, I will present how one can use this method in the study of Affleck-Kennedy-Lieb-Tasaki-like models, and in the latter half, I will show an attempt to modify the ansatz of the algorithm to Bethe ansatz for spin chains closed to integrable models.