3d TQFT from 6d SCFT

TL;DR

This paper explores how a six-dimensional superconformal field theory, when compactified on a three-manifold, reduces to a three-dimensional topological quantum field theory related to complex Chern-Simons theory, revealing new connections between high-dimensional SCFTs and 3D TQFTs.

Contribution

It demonstrates a novel reduction of 6d (2,0) SCFT to a 3D TQFT via compactification and twisting, establishing a link to complex Chern-Simons theory.

Findings

Reduction of 6d SCFT to 3D TQFT in large M limit

Connection established between 6d SCFT and complex Chern-Simons theory

Identification of supersymmetry preservation under compactification

Abstract

We study the six-dimensional (2,0) superconformal field theory on S^1 x S^2 x M via compactification to five dimensions, where M is a three-manifold. Twisted along M, the five-dimensional theory has a half of N = (2,2) supersymmetry on S^2, the other half being broken by a superpotential. We show that in the limit where M is infinitely large, the twisted theory reduces to a three-dimensional topological quantum field theory which is closely related to Chern-Simons theory for the complexified gauge group.