A note on W symmetry of N=2 gauge theory

TL;DR

This paper explores the W algebra symmetry in N=2 gauge theories via the AGT correspondence, focusing on how Toda CFT conformal blocks relate to gauge theory Casimir operators, with a detailed example involving W_3 symmetry.

Contribution

It analyzes the connection between Toda CFT conformal blocks and Casimir operators in N=2 gauge theories, emphasizing the role of W algebra symmetry, especially W_3.

Findings

Conformal blocks encode expectation values of Casimir operators.

W algebra symmetry structures are crucial in understanding gauge theory observables.

The A_2 Toda CFT with W_3 symmetry exemplifies these relationships.

Abstract

The AGT correspondence indicates $\mathcal{N}=2$ gauge theory possesses of W algebra symmetry. We study how the conformal block of Toda CFT gives the expectation value of Casimir operators of gauge theory. The $A_2$ Toda CFT with $W_3$ symmetry is taken as the main example.