AGT on the S-duality Wall

TL;DR

This paper explores how S-duality in four-dimensional N=4 SYM theories manifests in the three-dimensional gauge theory T[G] on a domain wall, linking it to Liouville conformal blocks through partition functions.

Contribution

It demonstrates that the mass deformation of T[G] induced by bulk N=2^* deformation relates to Liouville conformal blocks, revealing a new connection between gauge theory and conformal field theory.

Findings

Partition functions of T[SU(2)] match Liouville conformal blocks.

Mass deformation of T[G] corresponds to S-duality transformations.

The work links 3D gauge theories to 2D conformal field theories.

Abstract

Three-dimensional gauge theory T[G] arises on a domain wall between four-dimensional N=4 SYM theories with the gauge groups G and its S-dual G^L. We argue that the N=2^* mass deformation of the bulk theory induces a mass-deformation of the theory T[G] on the wall. The partition functions of the theory T[SU(2)] and its mass-deformation on the three-sphere are shown to coincide with the transformation coefficient of Liouville one-point conformal block on torus under the S-duality.