General relativity and the AKSZ construction
type: Item
instance of: scholarly article
title: General relativity and the AKSZ construction
zbMATH Open document ID: 1470.81055
author: G. Canepa
author: M. Schiavina
author: Alberto Cattaneo
published in: Communications in Mathematical Physics
publication date: 2021-07-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/2006.13078
review text: In the article under reviewing the authors apply the previous Alexandrov-Kontsevich-Schwarz-Zaboronski ( AKSZ) construction [\textit{M. Alexandrov} et al., Int. J. Mod. Phys. A 12, No. 7, 1405--1429 (1997; Zbl 1073.81655)] to the Batalin-Fradkin-Vilkovysky description of the reduced phase space both Einstein-Hilbert action and of the Palatini-Cartan theory in every space-time dimension greater than 2. The authors make a comparison between the case of Einstein-Hilbert and Palatini-Cartan cases. One found that in the previous ( PC) case one recover a Batalin-Vilkovysky theory for the first order formulation of an Einstein-Hilbert theory. While in the later case one agree with Batalin-Vilkovysky theory for Palatini-Cartan theory with partial implementation of the torsion-free condition. All the theories investigated here are Batalin-Vilkovysky versions of the same classical system on cilinders. The study given here have the advantage of giving a compatible BV-Batalin-Fradkin-Vilkovysky description which represents a necessary starting point for quantization in a presence of a boundary.
Mathematics Subject Classification ID: 81T70
Mathematics Subject Classification ID: 81V17
Mathematics Subject Classification ID: 83C47
Mathematics Subject Classification ID: 83C05
Mathematics Subject Classification ID: 58C50
Mathematics Subject Classification ID: 58D25
Mathematics Subject Classification ID: 70S05
Mathematics Subject Classification ID: 53Z05
zbMATH DE Number: 7374499
zbMATH Keywords: Batalin-Vilkovysky formalism
zbMATH Keywords: Alexandrov-Kontsevich-Schwarz-Zaboronski (AKSZ) construction
zbMATH Keywords: Einstein-Hilbert theory
zbMATH Keywords: Palatini-Cartan theory
zbMATH Keywords: torsion
zbMATH Keywords: quantization
reviewed by: Alex B. Gaina
MaRDI profile type: Publication
OpenAlex ID: W3036188108
arXiv ID: 2006.13078
cites work: The geometry of the master equation and topological quantum field theory.
cites work: Frame-like Lagrangians and presymplectic AKSZ-type sigma models
cites work: Local BRST cohomology in the antifield formalism. I: General theorems
cites work: Hamiltonian BRST and Batalin-Vilkovisky formalisms for second quantization of gauge theories
cites work: First order parent formulation for generic gauge field theories
cites work: A generalized canonical formalism and quantization of reducible gauge theories
cites work: GROUPOID SYMMETRY AND CONSTRAINTS IN GENERAL RELATIVITY
cites work: Quantum gravity from the point of view of locally covariant quantum field theory
cites work: BV equivalence between triadic gravity and BF theory in three dimensions
cites work: Classical BV theories on manifolds with boundary
cites work: Perturbative quantum gauge theories on manifolds with boundary
cites work: A cellular topological field theory
cites work: Split Chern–Simons Theory in the BV-BFV Formalism
cites work: Globalization for perturbative quantization of nonlinear split AKSZ sigma models on manifolds with boundary
cites work: BV-BFV approach to general relativity: Einstein-Hilbert action
cites work: On time
cites work: BV-BFV approach to general relativity: Palatini-Cartan-Holst action
cites work: The reduced phase space of Palatini-Cartan-Holst theory
cites work: Quantum Theory of Gravity. I. The Canonical Theory
cites work: Path-integral equivalence between the extended and nonextended Hamiltonian formalisms
cites work: Parent formulation at the Lagrangian level
cites work: Q4840214
cites work: Elimination of the auxiliary fields in the antifield formalism
cites work: Two-dimensional Yang-Mills theory on surfaces with corners in Batalin-Vilkovisky formalism
cites work: Towards holography in the BV-BFV setting
cites work: BFV-complex and higher homotopy structures
cites work: Homological reduction of constrained Poisson algebras
DOI: 10.1007/S00220-021-04127-6
Recommended article: Presymplectic AKSZ formulation of Einstein gravity
Recommended article: On the AKSZ formulation of the Poisson sigma model.
Recommended article: Quantum Chern-Simons theories on cylinders: BV-BFV partition functions
Recommended article: Finite-dimensional AKSZ-BV theories
Recommended article: BV analysis of Polyakov and Nambu-Goto theories with boundary
Recommended article: Globalization for perturbative quantization of nonlinear split AKSZ sigma models on manifolds with boundary
Recommended article: Canonical functions, differential graded symplectic pairs in supergeometry, and Alexandrov-Kontsevich-Schwartz-Zaboronsky sigma models with boundaries
Recommended article: A construction of observables for AKSZ sigma models
Recommended article: Introduction to the BV-BFV formalism
Recommended article: AKSZ-BV formalism and courant algebroid-induced topological field theories
description: scientific article