Q-Exact Actions for BF Theories

TL;DR

This paper proves that the actions for all classical and quantum BF theories on n-manifolds can be expressed as anti-commutators involving hermitian, nilpotent fermionic charges, with implications for observables.

Contribution

It demonstrates a universal formulation of BF theory actions using anti-commutators of fermionic charges, expanding the understanding of their structure.

Findings

Actions are given by anti-commutators of fermionic charges.

Enlargement of field space includes mass terms for Grassmann-odd fields.

Implications for observables in BF theories are discussed.

Abstract

The actions for all classical (and consequently quantum) $BF$ theories on $n$-manifolds is proven to be given by anti-commutators of hermitian, nilpotent, scalar fermionic charges with Grassmann-odd functionals. In order to show this, the space of fields in the theory must be enlarged to include ``mass terms'' for new, non-dynamical, Grassmann-odd fields. The implications of this result on observables are examined.