Presymplectic BV-AKSZ formulation of Conformal Gravity

TL;DR

This paper develops a presymplectic BV-AKSZ framework for conformal gravity, providing a novel, constraint-free, frame-like action formulation that extends to general gauge theories.

Contribution

It introduces a new presymplectic BV-AKSZ approach to conformal gravity, yielding a previously unknown, constraint-free, frame-like action consistent with the usual theory.

Findings

Identified a compatible presymplectic structure on the BRST complex

Derived a full-scale BV formulation without off-shell constraints

Extended the approach to generic gauge theories

Abstract

We elaborate on the presymplectic BV-AKSZ approach to local gauge theories and apply it to conformal gravity. More specifically, we identify a compatible presymplectic structure on the minimal model of the total BRST complex of this theory and show that together with the BRST differential it determines a full-scale BV formulation for a specific frame-like action which seems to be previously unknown. Remarkably, the underlying frame-like description requires no artificial off-shell constraints. Instead, the action becomes equivalent to the usual conformal gravity one, upon gauging away all the variables belonging to the kernel of the presymplectic structure. Finally, we show how the presymplectic BV-AKSZ approach extends to generic gauge theories.