Complex Chern-Simons from M5-branes on the Squashed Three-Sphere

TL;DR

This paper establishes a connection between the (2,0) superconformal M5-brane theory on a squashed three-sphere and complex Chern-Simons theory, revealing how geometric parameters influence gauge theory properties.

Contribution

It demonstrates an explicit equivalence between M5-brane reduction and complex Chern-Simons theory, including the role of squashing parameters in gauge symmetry and level structure.

Findings

Massless fermions act as ghosts for gauge fixing.

Squashing parameter controls the imaginary part of the Chern-Simons level.

Derived a second-order fermion action in the reduction.

Abstract

We derive an equivalence between the (2,0) superconformal M5-brane field theory dimensionally reduced on a squashed three-sphere, and Chern-Simons theory with complex gauge group. In the reduction, the massless fermions obtain an action which is second order in derivatives and are reinterpreted as ghosts for gauge fixing the emergent non-compact gauge symmetry. A squashing parameter in the geometry controls the imaginary part of the complex Chern-Simons level.