5D SYM and 2D q-Deformed YM

TL;DR

This paper explores a conjectured relation between 4D gauge theories and 2D q-deformed Yang-Mills theories using 5D supersymmetric Yang-Mills theory, confirming the conjecture through consistent results.

Contribution

It provides a novel derivation and confirmation of the AGT-like relation connecting 4D and 2D gauge theories via 5D supersymmetric Yang-Mills theory.

Findings

Results agree with the conjectured relations

Supports the 6D to 5D to 4D/2D theoretical chain

Validates the use of 5D SYM in understanding 4D/2D dualities

Abstract

We study the AGT-like conjectured relation of a four-dimensional gauge theory on the direct product of a three-sphere and a circle to two-dimensional q-deformed Yang-Mills theory on a Riemann surface by using a five-dimensional N=2 supersymmetric Yang-Mills theory on the direct product of the three-sphere and the Riemann surface, following the conjectured relation of the six-dimensional N=(2,0) theory on the circle to the five-dimensional Yang-Mills theory. Our results are in perfect agreement with both of the conjectures.