On 7D TFT and 6D chiral CFT

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 $\mathbb{N}=4$ supersymmetric Yang-Mills theory in four dimensions.

10 pages, v2: we have learned that the main results appear already in hep-th/0108152, see added notes at end of paper