3d Chern-Simons Theory from M5-branes

TL;DR

This paper demonstrates how 5d N=2 supersymmetric Yang-Mills theory on a product space reduces to complex Chern-Simons theory on a 3-manifold, providing a new derivation from M5-branes compactification.

Contribution

It explicitly derives the reduction of 5d N=2 theory to 3d complex Chern-Simons theory, confirming and extending the 3d/3d correspondence for various gauge groups.

Findings

Path integral reduces to 3d complex Chern-Simons theory

Confirms predictions from 3d/3d correspondence for SU(N)

Suggests generalization of the correspondence to other gauge groups

Abstract

We study 5d N=2 maximally supersymmetric Yang-Mills theory with a gauge group G on S^2 x M_3, where M_3 is a 3-manifold. By explicit localization computation we show that the path-integral of the 5d N=2 theory reduces to that of the 3d G_C Chern-Simons theory on M_3, where G_C is the complexification of G. This gives a direct derivation of the appearance of the Chern-Simons theory from the compactification of the 6d (2,0) theory, confirms the predictions from the 3d/3d correspondence for G=SU(N), and suggests the generalization of the correspondence to more general gauge groups.