On AGT Conjecture for Pure Super Yang-Mills and W-algebra

TL;DR

This paper explores the connection between pure super Yang-Mills theory and W_3-algebra, proposing a relation between the Shapovalov matrix and Nekrasov partition functions, extending AGT conjecture insights.

Contribution

It introduces a novel relation linking the Shapovalov matrix of W_3-algebra to Nekrasov partition functions for N=2 SU(3) Yang-Mills theory.

Findings

Proposes a simple relation between W_3-algebra and Nekrasov functions.

Extends AGT conjecture to pure super Yang-Mills case.

Provides a new algebraic approach to gauge theory partition functions.

Abstract

Recently Alday, Gaiotto and Tachikawa have proposed relation between 2- and 4-dimensional conformal field theories. The relation implies that the Nekrasov partition functions of N=2 superconformal gauge theories are equal to conformal blocks associated with the conformal algebra. Likewise, a counterpart in pure super Yang-Mills theory exists in conformal field theory. We propose a simple relation between the Shapovalov matrix of the W_3-algebra and the Nekrasov partition function of N=2 SU(3) Yang-Mills theory.