Titles, Abstracts and Slides
January 8 (Sat)
Atsuo Kuniba (Tokyo) [PDF (1.5MB)]
Title: 30 years of box-ball systems
Abstract: Box-ball system (BBS) is an integrable cellular automaton in one dimension introduced in 1990. I review its main developments that took every couple of years in the past 30 years along ultradiscretization, crystal theory in quantum groups, combinatorial Bethe ansatz, thermodynamic Bethe ansatz and generalized hydrodynamics including the latest result on the large deviations based on joint works with Grégoire Misguich and Vincent Pasquier.
Mayuko Yamashita (RIMS) [PDF (13.5MB)]
Title: On the absence of all heterotic global anomalies
Abstract: In this talk, I will explain the work "Topological modular forms and the absence of all heterotic global anomalies" (https://arxiv.org/abs/2108.13542) with Yuji Tachikawa from a mathematical point of view. That work is aimed at settling a physical problem to show the vanishing of anomalies in heterotic string theories. We translate the problem into a mathematical problem to show that a certain transformation of generalized cohomology theories from TMF (Topological Modular Forms) to the Anderson dual to String bordism, and prove that it is indeed the case. Here, the Anderson dual of a generalized homology theory plays the crucial role in the classification of anomalies by a conjecture of Freed and Hopkins. I will also explain this point, as well as related works on the Anderson duals.
Tadashi Takayanagi (Kyoto) [PDF (939KB)]
Title: Holography in de Sitter Space via Chern-Simons Gauge Theory
Abstract: We propose a holographic duality for classical gravity on a three-dimensional de Sitter space. We first show that a pair of SU(2) Chern-Simons gauge theories reproduces the classical partition function of Einstein gravity on a Euclidean de Sitter space, namely a three dimensional sphere, when we take the limit where the level k approaches -2. This implies that the CFT dual of gravity on a de Sitter space at the leading semi-classical order is given by an SU(2) Wess-Zumino-Witten (WZW) model in the large central charge limit k→-2. We give another evidence for this in the light of known holography for coset CFTs. We also present a higher spin gravity extension of our duality.
Giulio Bonelli (SISSA)
Title: Black hole perturbation theory from classical CFT2 and gauge theories
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, it reduces to the study of ordinary second order differential equations. As already observed long ago by A. M. Polyakov, these 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 ODE and give novel exact and explicit formulas for the grey body factor, quasi-normal modes and Love numbers of the Kerr black hole.
January 9 (Sun)
Kazunobu Maruyoshi (Seikei) [PDF (505KB)]
Title: L-operators in integrable models and defects
Abstract: In this talk, we discuss relationship between L-operators in integrable models and defects in four-dimensional supersymmetric quantum field theories. The L-operators we discuss satisfy the RLL relation with the elliptic R matrix encoding Boltzmann weights of two-dimensional integrable lattice model (eight-vertex model and its generalization). The transfer matrices of these L-operators are identified with defects in four-dimensional supersymmetric theories on certain manifolds. The one is half-BPS surface defects in N=1 and N=2 supersymmetric gauge theory on S^1 \times Lens space, and the other is half-BPS (Wilson-'t Hooft) line defects in N=2 supersymmetric gauge theory on S^1 \times omega-deformed R^3. A reason of this relation is the both defect configurations are embedded in string/M-theory and dual to the one induces four-dimensional Chern-Simons theory where the relation with integrable models are argued by Costello, Yamazaki and Witten. This talk is based on arXiv:1606.01041, arXiv:2009.12391 and a collaboration with Toshihiro Ota and Masahito Yamazaki.
Yukinobu Toda (IPMU) [PDF (104KB)]
Title: Categorical wall-crossing formula in Donaldson-Thomas theory
Abstract: The Donaldson-Thomas invariants virtually count stable objects on Calabi-Yau 3-folds, and their wall-crossing phenomena is important both in mathematics and physics. In this talk, I will discuss conjectural categorifications of DT invariants to some dg-categories, and their categorical wall-crossing formula. I will propose some rather vague conjectures on the categorification problem, explain that many of them are rigorous theorem for local surfaces, and describe the categorical wall-crossing formula in the case of the resolved conifold.
Zohar Komargodski (Stony Brook) [PDF (762KB)]
Title: Aspects of line defects in d dimensions
Abstract: We consider renormalization group flows on line defects in d dimensions. We define a "defect entropy'' and argue that it decreases monotonically during RG flows. We apply this result to line defects which appear in condensed matter and high energy physics, including magnetic (SPT) defects, localized field defects, and Wilson loops. In some of these cases we make some new experimental predictions and in the case of Wilson lines we make some comparisons with localization and holography.
January 10 (Mon)
Shota Komatsu (CERN) [PDF (1.4MB)]
Title: Crosscap States in Integrable Field Theories and Spin Chains
Abstract: Crosscap states have been extensively studied in two-dimensional conformal field theory in the past, where part of the motivations came from their connection to orientifolds in string theory. Surprisingly, however, analogous studies in integrable field theories have been lacking. In this talk, I will fill this gap by presenting a systematic study of crosscap states in integrable field theories and spin chains. First, I derive an exact formula for overlaps between the crosscap state and any excited state in integrable field theories with diagonal scattering. Using the formula, I compute the crosscap entropy i.e. the overlap with the ground state in several examples, and find that it decreases monotonically along the renormalization group flow except in cases where the discrete symmetry is spontaneously broken in the infrared. We next introduce crosscap states in integrable spin chains and obtain exact determinant expressions for overlaps with energy eigenstates. These states are long-range entangled and provide interesting initial conditions for the quantum quench protocol, which are quite distinct from short-range entangled states corresponding to the boundary states. As a side result, I will also briefly comment on the interplay between fermionization and Bethe ansatz.
Alexei Borodin (MIT) [PDF (8.5MB)]
Title: sl(1|1)-vertex models: boson-fermion correspondence and determinantal point processes
Mikhail Kapranov (IPMU) [PDF (236KB)]
Title: Perverse schobers and the Algebra of the Infrared
Abstract: The term "Algebra of the Infrared" was coined by Gaiotto, Moore and Witten to signify a novel algebraic structure with strong polyhedral flavor that they discovered. It relates various categorical data of a massive 2d supersymmetric theory.
We argue that the natural mathematical framework for this structure is the concept of perverse schobers, categorical analogs of perverse sheaves. A perverse schober F on the complex line C (having the meaning of the plane of central charges) has, first, the vanishing cycle categories (corresponding to the local D-brane categories at the vacua) and the transport functors (corresponding to tunneling between the vacua).
The constructions of the Algebra of the Infrared can be seen, in our approach, as providing the analog of the Fourier-Sato transform for F. The appearance of convex geometry becomes very natural from the Fourier transform point of view (behavior of the exponentials in the complex domain). The talk is based on joint work with Y. Soibelman and L. Soukhanov, arXiv 2011.00845.