Compactification on the \Omega-background and the AGT correspondence

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.