Compactification on the \Omega-background and the AGT correspondence

TL;DR

This paper explores how compactifying the six-dimensional (2,0) theory in the -background leads to a chiral gauged WZW model, revealing connections to the AGT correspondence and Seiberg-Witten curves.

Contribution

It demonstrates that the effective theory from compactification naturally contains the W-algebra related to the AGT correspondence, linking 6D theories to 2D conformal models.

Findings

The effective theory is a chiral gauged WZW model.

The W-algebra symmetry encodes the AGT correspondence.

Expectation values of currents determine Seiberg-Witten curves.

Abstract

The six-dimensional (2,0) theory formulated in the \Omega-background gives rise to two-dimensional effective degrees of freedom. By compactifying the theory on the circle fibers of two cigar-like manifolds, we find that a natural candidate for the effective theory is a chiral gauged WZW model. The symmetry algebra of the model contains the W-algebra that appears on the two-dimensional side of the AGT correspondence. We show that the expectation values of its currents determine the Seiberg-Witten curve of the four-dimensional side.