BV-equivalence between triadic gravity and BF theory in three dimensions

TL;DR

This paper establishes an explicit off-shell BV symplectomorphism demonstrating the equivalence between triadic gravity and BF theory in three dimensions, clarifying their symmetry structures.

Contribution

It provides the first explicit off-shell BV symplectomorphism linking triadic gravity and BF theory in three dimensions, enhancing understanding of their equivalence.

Findings

Off-shell BV symplectomorphism between the two theories

Clarification of symmetry structures in both theories

Explicit mapping of BV formulations

Abstract

The triadic description of General Relativity in three dimensions is known to be a BF theory. Diffeomorphisms, as symmetries, are easily re- covered on shell from the symmetries of BF theory. This note describes an explicit off-shell BV symplectomorphism between the BV versions of the two theories, each endowed with their natural symmetries.