AGT on the S-duality wall

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.