Topological Quantum Field Theory on Non-Abelian Gerbes

TL;DR

This paper constructs a BRST operator for non-Abelian gerbes, linking topological quantum field theory, cohomology, and universal gerbes, and discusses the construction of observables within this framework.

Contribution

It introduces a nilpotent BRST operator for non-Abelian gerbes and relates it to the universal gerbe and cohomological structures, advancing the understanding of topological quantum field theories.

Findings

BRST operator for non-Abelian gerbes constructed

Connection between BRST operator and Cech-de Rham complex established

Insights into observables in topological quantum field theory provided

Abstract

The infinitesimal symmetries of a fully decomposed non-Abelian gerbe can be generated in terms of a nilpotent BRST operator, which is here constructed. The appearing fields find a natural interpretation in terms of the universal gerbe, a generalisation of the universal bundle. We comment on the construction of observables in the arising Topological Quantum Field Theory. It is also shown how the BRST operator and the trace part of a suitably truncated set of fields on the non-Abelian gerbe reduce directly to the coboundary operator and the pertinent cochains of the underlying Cech-de Rham complex.