Edge Dynamics for BF Theories and Gravity

TL;DR

This paper explores boundary conditions and boundary actions in BF theories and gravity, emphasizing the importance of boundary terms for well-defined variational principles and potential links to membrane paradigms.

Contribution

It introduces a systematic method to determine boundary actions in BF theories and gravity, highlighting the role of boundary terms for different boundary conditions.

Findings

Boundary terms are essential for well-defined variational principles.

Boundary actions for gravity can be derived using this approach.

Discussion of potential connections to membrane paradigm.

Abstract

We discuss BF theories defined on manifolds with spatial boundaries. Variational arguments show that one needs to augment the usual action with a boundary term for specific types of boundary conditions. We also show how to use this procedure to find the boundary actions for theories of gravity with first order formulations. Possible connection with the membrane approach is also discussed.