List of Talks
Bufan Zheng : An Introduction to Pure Spinor Formalism with application to Tree-Level String Amplitudes Slide
Abstract: There are three well-known formalisms for superstring theory: RNS, Green-Schwarz, and pure spinor. This talk will focus on the pure spinor formalism and its application in computing n-point tree-level string amplitudes of massless states. If time allows, the talk will extend to cover the color-kinematics duality in gauge theories, the double copy relations, and the construction of BCJ numerators for 10-dimensional super Yang-Mills theory using the pure spinor formalism.
Mikito Shimoda : 4-dimensional gauge theory in mathematics
Abstract: In mathematics, 4-dimensional gauge theory is priamarily applied to study topology of 4-manifolds. I will outline the methodology, focusing specifically on Donaldson theory.
Kouki Kumagai : Factorization algebras in operator formalism
Abstract: Field theory is a fundamental framework of modern physics, appearing in diverse areas such as particle physics, condensed matter theory, and cosmology. Despite its decisive importance, however, a complete mathematical formulation of field theory has not yet been achieved. Broadly speaking, there are two major approaches to field theory: the operator formalism and the path integral formalism. A mathematical theory that unifies these two perspectives is regarded as essential for a genuine formulation of field theory. Over the years, various mathematical formulations have been proposed for each of these approaches. Segal’s axioms provide a geometric formulation of the operator formalism, though it does not provide a general correspondence with the path integral. On the other hand, the Batalin–Vilkovisky (BV) formalism gives an algebraic treatment of perturbation theory based on path integrals. The factorization algebra framework developed by Costello and Gwilliam incorporates the BV formalism while capturing geometric features similar to those in Segal’s axioms, providing a systematic perturbative formulation. However, they did not explicitly describe how to derive the operator formalism, and clarifying their relationships remains an open problem. In this talk, I will present my recent considerations on how factorization algebras encode the operator formalism.
Ching-Yu Yao : Lattice Translation Modulated Symmetries and TFTs
Abstract: Modulated symmetries are internal symmetries that are not invariant under spacetime symmetry actions. In this talk, I will propose a general way to describe 1+1D quantum systems with lattice translation modulated symmetries, including the non-invertible ones, via the tensor network language. Moreover, even the topological behaviors of the modulated symmetries are broken, I will demonstrate how to construct the modulated version of the symmetry TFT bulks. This structure not only recovers some known results on invertible modulated symmetries, but also provides a framework to tackle modulated symmetries in a more general setting.
Dongao Zhou : Some Aspects of Supersymmetric Localization
Abstract: I will give a pedagogical introduction to supersymmetry localization in quantum field theory, and explain how the generic framework is applied to topological quantum field theories. In particular, I will motivate how K-theory and elliptic cohomology could be related to supersymmetric quantum field theories. If time permits, I will also discuss Costello’s holomorphically twisted 4d N=1 SYM theory with Yangian deformation from the perspective of supersymmetric quantum field theories.
Yi Zhang : Anomalies and fermionic unitary operators Slide
Abstract: I will review some facts about position-dependent U(1) transformations of two-dimensional theories with U(1) anomaly of odd level. To illustrate, we give multiple derivations of the fact that position-dependent are fermionic when the winding number is odd. We then relate this mechanism to the anomalies of the discrete Z_N ⊂ U(1) symmetry, whose description also crucially uses unitary operators which are fermionic. Time permits, I will also discuss how position-dependent SU(2) transformations of four-dimensional theories with SU(2) symmetry with Witten anomaly are fermionic and anticommute among themselves when the winding number is odd.
Masataka Watanabe : Effective solutions to the Theory of Everything
Abstract: I will explain the power of symmetry and effective field theory to understand various phenomena in nature.
Yuan Miao : On the Haldane--Shastry model
Abstract: The Haldane--Shastry (HS) model is an exactly solvable spin chain with long-range interaction. It can be viewed as the freezing limit of the spin Calogero--Sutherland model. There are various motivations to study the HS model. A particular reason is that the HS model has a Yangian symmetry on the lattice, where the spectrum and degeneracies have nice representation theory/combinatorics origin. I will explain how to obtain the complete spectrum as well as the Yangian highest-weight states in the literature. Then I will present some new results on how to construct the Yangian descendant states (by diagonalising a twisted transfer matrix) using algebraic Bethe ansatz (ABA), analogous to an inhomogeneous XXX spin chain. Knowing the ABA, we are able to find the norm and overlap between the Yangian descendant states. If time permits, I will also discuss the relations between the HS model and the $\mathfrak{su}(2)_1$ WZW CFT, which has a hidden Yangian symmetry discovered in the 90's. The novel results are based on an ongoing collaboration with Jean-Sébastien Caux, Yunfeng Jiang and Jules Lamers.
Jiakang Bao : Induced Higgs Mechanism in 6d and Class S
Abstract: I will discuss the class S theories and how they arise from 6d under compactifications. Many quantities would be preserved, and we can check that if they would agree in 6d and in 4d. In particular, the magnetic quivers, which can read off directly from the information of the punctures or obtained from the brane pictures, serve as a useful tool in the study of Higgsings. We shall compare the Higgsing algorithms from 6d and from magnetic quivers. The story is well-known for A-type cases. If time permits, I shall mention some recent work in progress with Noppadol Mekareeya, Gabi Zafrir and Hao Zhang on the D-type cases.