Hitchin systems, N=2 gauge theories and W-gravity

TL;DR

This paper explores the deep connection between N=2 gauge theories, Hitchin systems, and W-gravity, proposing an M-theory perspective that links conformal field theories with gauge theory moduli spaces.

Contribution

It introduces an M-theory derivation of the AGT duality, identifying Toda field theory with moduli of M5-branes and relating gauge theory operators to W-algebra currents.

Findings

Nekrasov's partition function satisfies W-geometry constraints

Chiral operators correspond to W-algebra currents

Toda field theory quantizes M5-brane moduli

Abstract

We propose some arguments supporting an M-theory derivation of the duality recently discovered by Alday, Gaiotto and Tachikawa between two-dimensional conformal field theories and N=2 superconformal gauge theories in four dimensions. We find that A_{N-1} Toda field theory is the simplest two-dimensional conformal field theory quantizing the moduli of N M5-branes wrapped on a Riemann surface. This leads us to identify chiral operators of the N=2 gauge theories with W-algebra currents. As a check of this correspondence we study some relevant OPE's obtaining that Nekrasov's partition function satisfies W-geometry constraints.