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Representation theory of W-algebras and Higgs branch conjecture

Tomoyuki Arakawa

Abstract

We survey a number of results regarding the representation theory of $W$-algebras and their connection with the resent development of the four dimensional $N=2$ superconformal field theories in physics.

Representation theory of W-algebras and Higgs branch conjecture

Abstract

We survey a number of results regarding the representation theory of -algebras and their connection with the resent development of the four dimensional superconformal field theories in physics.

Paper Structure

This paper contains 6 sections, 11 theorems, 31 equations.

Table of Contents

  1. Introduction
  2. Vertex algebras
  3. $W$-algebras
  4. Representation theory of $W$-algebras
  5. BRST reduction of associated varieties
  6. The rationality of minimal series principal W-algerbas

Key Result

Theorem 1

Let $f_{min}\in \mathbb{O}_{min}$ and let $k$ be an arbitrary complex number.

Theorems & Definitions (13)

  • Theorem 1: Ara05
  • Remark 2
  • Theorem 3: Ara09b
  • Theorem 4: Ara07
  • Theorem 5: Ara09b
  • Theorem 6: Ara09b
  • Theorem 7: Ara09b
  • Theorem 8: A2012Dec
  • Theorem 9: A12-2
  • Theorem 10: ACL17
  • ...and 3 more