On AGT description of N=2 SCFT with N_f=4

TL;DR

This paper explores the AGT correspondence for N=2 SU(2) gauge theory with four flavors, analyzing how SO(8) flavor symmetry Weyl transformations are realized in Liouville theory, providing consistency checks and insights into surface operators and WZW theory.

Contribution

It demonstrates the realization of SO(8) Weyl symmetry in Liouville four-point functions, offering a non-trivial consistency check of the AGT conjecture for N=2 SCFT with N_f=4.

Findings

Weyl symmetry transformations correspond to functional properties of Liouville four-point functions

Provides a consistency check for the AGT conjecture in this context

Comments on elementary surface operators and WZW theory connections

Abstract

We consider Alday-Gaiotto-Tachikawa (AGT) realization of the Nekrasov partition function of N=2 SCFT. We focus our attention on the SU(2) theory with N_f=4 flavor symmetry, whose partition function, according to AGT, is given by the Liouville four-point function on the sphere. The gauge theory with N_f=4 is known to exhibit SO(8) symmetry. We explain how the Weyl symmetry transformations of SO(8) flavor symmetry are realized in the Liouville theory picture. This is associated to functional properties of the Liouville four-point function that are a priori unexpected. In turn, this can be thought of as a non-trivial consistency check of AGT conjecture. We also make some comments on elementary surface operators and WZW theory.