연사: Wenjun Niu (Perimeter Institute)

장소: 129-406

시간:
2026-07-27(월) 10:00~11:30

2026-07-27(월) 14:00~15:30

2026-07-29(수) 10:00~11:30

Title:   Defects of 4d N=2 field theories and representation theory.

Abstract: 4d N=2 field theories is a rich source of new mathematics. In this series of talks, I will focus on the holomorphic-topological twist of these theories, and explore the (higher) algebra of defects, particularly the category of line defects. Along the way, I will report on work in progress/to appear with various collaborators on the representation-theoretic aspects of these defects. The following is a break-down of the plan of the lectures. The lectures will be mildly connected to each other.  

1. This lecture will be mostly about background materials. I will start with reviewing the HT twist of 4d N=2 gauge theories in the BV formalism. Using this, I will explain how to give a systematic yet abstract definition of defects of various dimensions, and highlight the algebraic structures they carry. I will also discuss compactifications of the theory and what happens to defects under these compactifications.  

2. In the second lecture, I will consider boundary conditions of the 4d pure gauge theories given by linear representations of the gauge group, possibly deformed by a potential. I will explain how the action of bulk lines on such boundary lines realizes the chiral ring relations of Nekrasov-Shatashivili. This is based on joint work to appear with J. Hilburn. 

3. I will explore possibly non-Lagrangian 4d HT theories using cohomological Hall algebras. After reviewing the definition and properties of these algebras, as well as their string-theoretic interpretation, I will explain a proposal to define the category of line operators of the 4d HT theory using these algebras. This is based on joint work to appear with S. DeHority and A. Latyntsev. When the CoHA corresponds to a Lagrangian gauge theory, we formulate a conjecture relating our proposed category and the category of Cautis-Williams. I will discuss an idea to tackle this conjecture using the results of the second lecture. This is a work very much in progress with D. Gaiotto and J. Hilburn.