On the symmetries of BF models and their relation with gravity

TL;DR

This paper explores the extension of vector supersymmetry in BF models to general manifolds and investigates its implications for understanding the relationship between BF models and gravity, especially in three dimensions.

Contribution

It extends vector supersymmetry to generic manifolds within the Batalin-Vilkovisky framework and analyzes its connection to gravity in three-dimensional space-time.

Findings

Vector supersymmetry can be incorporated into BF models on arbitrary manifolds.

The relationship between gravity and BF models is clarified in three-dimensional space-time.

Potential implications for quantum gravity are discussed.

Abstract

The perturbative finiteness of various topological models (e.g. BF models) has its origin in an extra symmetry of the gauge-fixed action, the so-called vector supersymmetry. Since an invariance of this type also exists for gravity and since gravity is closely related to certain BF models, vector supersymmetry should also be useful for tackling various aspects of quantum gravity. With this motivation and goal in mind, we first extend vector supersymmetry of BF models to generic manifolds by incorporating it into the BRST symmetry within the Batalin-Vilkovisky framework. Thereafter, we address the relationship between gravity and BF models, in particular for three-dimensional space-time.