Deformation of BF theories, Topological Open Membrane and A Generalization of The Star Deformation

TL;DR

This paper explores deformations of BF theories using antifield BRST formalism, leading to new topological gauge theories and noncommutative structures on open membrane boundaries, generalizing star deformation concepts.

Contribution

It introduces a new class of topological gauge theories via BF theory deformations and connects them to noncommutative boundary structures of open membranes.

Findings

Identified consistent interaction terms for deformed BF theories.

Established a link between BF deformations and noncommutative boundary structures.

Proposed a generalization of the star deformation path integral.

Abstract

We consider a deformation of the BF theory in any dimension by means of the antifield BRST formalism. Possible consistent interaction terms for the action and the gauge symmetries are analyzed and we find a new class of topological gauge theories. Deformations of the world volume BF theory are considered as possible deformations of the topological open membrane. Therefore if we consider these theories on open membranes, we obtain noncommutative structures of the boundaries of open membranes, and we propose a generalization of the path integral representation of the star deformation.