4d partition function on S^1 x S^3 and 2d Yang-Mills with nonzero area

TL;DR

This paper demonstrates that the 6d N=(2,0) theory compactified on S^1 x S^3 x C_2 reduces to 2d q-deformed Yang-Mills theory with finite area, extending previous results by explicitly computing the partition function.

Contribution

It provides a detailed derivation of the reduction from 6d N=(2,0) theory to 2d q-deformed Yang-Mills on C_2 at finite area, including the computation of the S^1 x S^3 partition function.

Findings

Reduction from 6d N=(2,0) theory to 2d q-deformed Yang-Mills.

Explicit computation of the partition function on S^1 x S^3.

Connection between 4d N=2 sigma model and 2d Yang-Mills propagator.

Abstract

We argue that 6d N=(2,0) theory on S^1 x S^3 x C_2 reduces to the 2d q-deformed Yang-Mills on C_2 at finite area, as a small extension to the result of Gadde, Rastelli, Razamat and Yan. This is done by computing the partition function on S^1 x S^3 of 4d N=2 supersymmetric non-linear sigma model on T^*G_C, which gives the propagator of the 2d Yang-Mills.