Parent formulation at the Lagrangian level

TL;DR

This paper introduces a parent formulation at the Lagrangian level for diffeomorphism-invariant theories, connecting it to AKSZ sigma models, BV-BRST, and Hamiltonian formalisms, with applications to various physical theories.

Contribution

It develops a Lagrangian parent formulation specialized for diffeomorphism-invariant theories, linking it to AKSZ models and extending the BV-BRST approach.

Findings

Formulation as an AKSZ-type sigma model for diffeomorphism-invariant theories

Unification of Lagrangian, BV-BRST, and Hamiltonian formalisms

Illustrated with examples including gravity and Yang-Mills

Abstract

The recently proposed first-order parent formalism at the level of equations of motion is specialized to the case of Lagrangian systems. It is shown that for diffeomorphism-invariant theories the parent formulation takes the form of an AKSZ-type sigma model. The proposed formulation can be also seen as a Lagrangian version of the BV-BRST extension of the Vasiliev unfolded approach. We also discuss its possible interpretation as a multidimensional generalization of the Hamiltonian BFV--BRST formalism. The general construction is illustrated by examples of (parametrized) mechanics, relativistic particle, Yang--Mills theory, and gravity.