Gravity as BF theory plus potential

TL;DR

This paper proposes a new formulation of gravity as a BF theory with an added potential term, which generalizes Plebanski's approach and retains key gravitational features, potentially aiding spin foam quantization and renormalization.

Contribution

It introduces a novel formulation of gravity as BF theory plus a potential, broadening the class of models suitable for spin foam quantization and addressing renormalization issues.

Findings

Recovering general relativity with an infinitely steep potential

Propagates two graviton polarizations in the generalized theory

Potentially facilitates spin foam quantization and renormalization

Abstract

Spin foam models of quantum gravity are based on Plebanski's formulation of general relativity as a constrained BF theory. We give an alternative formulation of gravity as BF theory plus a certain potential term for the B-field. When the potential is taken to be infinitely steep one recovers general relativity. For a generic potential the theory still describes gravity in that it propagates just two graviton polarizations. The arising class of theories is of the type amenable to spin foam quantization methods, and, we argue, may allow one to come to terms with renormalization in the spin foam context.