On 7D TFT and 6D chiral CFT

TL;DR

This paper analyzes a 7D Chern-Simons theory, showing it induces a chiral two-form on a 6D boundary, and discusses similar phenomena in 5D theories related to 4D supersymmetric Yang-Mills.

Contribution

It provides a canonical and BRST analysis of 7D Chern-Simons theory and reveals its boundary dynamics, connecting higher-dimensional topological theories to lower-dimensional chiral forms.

Findings

7D Chern-Simons induces a chiral two-form on 6D boundary

Analysis uses canonical and BRST methods

Comments on 5D Chern-Simons relevance to 4D SYM

Abstract

We perform a canonical and BRST analysis of a seven-dimensional Chern-Simons theory on a manifold with boundary. The main result is that the 7D theory induces for consistency a chiral two-form on the 6D boundary. We also comment on similar behaviour in a five-dimensional Chern-Simons theory relevant for $\N=4$ supersymmetric Yang-Mills theory in four dimensions.