(Super)gravity and Yang-Mills Theories as Generalized Topological Fields with Constraints

TL;DR

This paper develops a unified framework for generalized topological field theories with constraints, applying it to gravity, Yang-Mills, and supergravity, and explores boundary Chern-Simons actions.

Contribution

It introduces a generalized differential calculus approach to formulate constrained topological field theories, unifying various models including gravity and supergravity.

Findings

Reformulation of BF theories as constrained topological theories

Application to N=1,2 chiral supergravities

Boundary Chern-Simons actions naturally emerge from the bulk theory

Abstract

We present a general approach to construct a class of generalized topological field theories with constraints by means of generalized differential calculus and its application to connection theory. It turns out that not only the ordinary BF formulations of general relativity and Yang-Mills theories, but also the N=1,2 chiral supergravities can be reformulated as these constrained generalized topological field theories once the free parameters in the Lagrangian are specially chosen. We also show that the Chern-Simons action on the boundary may naturally be induced from the generalized topological action in the bulk, rather than introduced by hand.