General Relativity and the AKSZ construction

Abstract

In this note the AKSZ construction is applied to the BFV description of the reduced phase space of the Einstein-Hilbert and of the Palatini--Cartan theories in every space-time dimension greater than two. In the former case one obtains a BV theory for the first-order formulation of Einstein--Hilbert theory, in the latter a BV theory for Palatini--Cartan theory with a partial implementation of the torsion-free condition already on the space of fields. All theories described here are BV versions of the same classical system on cylinders. The AKSZ implementations we present have the advantage of yielding a compatible BV-BFV description, which is the required starting point for a quantization in presence of a boundary.

Improved version with new results about Palatini-Cartan theory. 41 Pages

References in corpus (5)

• First order parent formulation for generic gauge field theories
• Parent formulation at the Lagrangian level
• Boundary structure of General Relativity in tetrad variables
• Lectures on Batalin-Vilkovisky formalism and its applications in topological quantum field theory
• Presymplectic structures and intrinsic Lagrangians

Cited by in corpus (8)

• Boundary structure of General Relativity in tetrad variables
• Asymptotic symmetries in the BV-BFV formalism
• Presymplectic AKSZ formulation of Einstein gravity
• BV equivalence with boundary
• Gravity with torsion as deformed $BF$ theory
• Corner Structure of Four-Dimensional General Relativity in the Coframe Formalism
• Boundary structure of the standard model coupled to gravity
• BV Quantization