A note on topological brane theories

TL;DR

This paper explores the structure of topological p-brane theories, analyzing their canonical and BRST properties, and establishing connections to known topological field theories in flat backgrounds.

Contribution

It provides a detailed analysis of the canonical and BRST structures of topological p-brane theories and relates them to existing topological field theories in specific backgrounds.

Findings

Topological p-brane theories have no local degrees of freedom.

In flat backgrounds, p-brane theories relate to known topological field theories.

Equivalent actions for topological p-brane theories can be constructed.

Abstract

We consider the theory of closed $p$-branes propagating on $(p+1)$-dimensional space-time manifolds. This theory has no local degrees of freedom. Here we study its canonical and BRST structures of the theory. In the case of locally flat backgrounds one can show that the $p$-brane theory is related to another known topological field theory. In the general situation some equivalent actions can also be written for the topological $p$-brane theory.