BV Pushforward of Palatini-Cartan gravity

TL;DR

This paper demonstrates that the BV formulation of Palatini-Cartan gravity can be transformed into an AKSZ-like model compatible with boundary BFV data through a BV pushforward, linking different formalisms of gravity.

Contribution

It introduces a BV pushforward method to relate the standard BV gravity formalism to an AKSZ-like boundary-compatible model, providing a new perspective on gravity's mathematical structure.

Findings

Establishes equivalence between BV and AKSZ-like formulations of gravity

Provides a method to incorporate boundary data in gravity models

Bridges different mathematical frameworks for gravity theories

Abstract

The goal of this note is to show that the standard BV formulation of gravity in the Palatini-Cartan formalism is equivalent, using a BV pushforward, to an AKSZ-like version compatible with BFV data on the boundary.