Gauge/Vortex duality and AGT

TL;DR

This paper explores a triality connecting 4D gauge theories, vortex theories, and conformal field theories, providing proofs for parts of the AGT correspondence and extending it to 5D gauge theories.

Contribution

It introduces a novel triality framework that elucidates the AGT correspondence and generalizes it to five-dimensional gauge theories.

Findings

Proof of some cases of the AGT-correspondence

Establishment of a triality between gauge, vortex, and conformal theories

Extension of AGT to five-dimensional gauge theories

Abstract

This is the 12th article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories" ed. J. Teschner. This article describes one way to understand an important part of the AGT-correspondence in terms of a triality between four-dimensional gauge theory, the two-dimensional theory of its vortices, and conformal field theory. This triality is related to, and inspired by known large $N$ dualities of the topological string. It leads to a proof of some cases of the AGT-correspondence, and most importantly, of a generalisation of this correspondence to certain five-dimensional gauge theories.