Presymplectic AKSZ formulation of Einstein gravity

Abstract

Any local gauge theory can be represented as an AKSZ sigma model (upon parameterization if necessary). However, for non-topological models in dimension higher than 1 the target space is necessarily infinite-dimensional. The interesting alternative known for some time is to allow for degenerate presymplectic structure in the target space. This leads to a very concise AKSZ-like representation for frame-like Lagrangians of gauge systems. In this work we concentrate on Einstein gravity and show that not only the Lagrangian but also the full-scale Batalin--Vilkovisky formulation is naturally encoded in the presymplectic AKSZ formulation, giving an elegant supergeometrical construction of BV for Cartan-Weyl action. The same applies to the main structures of the respective Hamiltonian BFV formulation.

arXiv commentnotations updated, typos corrected, 23 pages

References in corpus (35)

• The Geometry of the Master Equation and Topological Quantum Field Theory
• Introduction to sh Lie algebras for physicists
• Local BRST cohomology in gauge theories
• A path integral approach to the Kontsevich quantization formula
• Local BRST cohomology in the antifield formalism: I. General theorems
• Geometry of jet spaces and integrable systems
• Higher order singletons, partially massless fields and their boundary values in the ambient approach
• Edge modes of gravity -- II: Corner metric and Lorentz charges
• Local BRST cohomology in Einstein--Yang--Mills theory
• Parent field theory and unfolding in BRST first-quantized terms
• Local BRST cohomology and covariance
• Lagrange structure and quantization
• Edge modes of gravity. Part III. Corner simplicity constraints
• Classical BV theories on manifolds with boundary
• BRST theory without Hamiltonian and Lagrangian
• Superfield BRST Charge and the Master Action
• A Poincare lemma for sigma models of AKSZ type
• A minimal BV action for Vasiliev's four-dimensional higher spin gravity
• First order parent formulation for generic gauge field theories
• Parent formulations, frame-like Lagrangians, and generalized auxiliary fields
• Algebraic structure of Gravity with Torsion
• Hamiltonian BRST and Batalin-Vilkovisky formalisms for second quantization of gauge theories
• Notes on the ambient approach to boundary values of AdS gauge fields
• Frame-like Lagrangians and presymplectic AKSZ-type sigma models
• Type-B Formal Higher Spin Gravity
• Parent formulation at the Lagrangian level
• Gauge PDE and AKSZ-type Sigma Models
• Asymptotic symmetries in the BV-BFV formalism
• Towards holography in the BV-BFV setting
• BV-BFV approach to General Relativity: Palatini-Cartan-Holst action
• Finite dimensional AKSZ-BV theories
• Presymplectic current and the inverse problem of the calculus of variations
• Ghost Equations and Diffeomorphism Invariant Theories
• General Relativity and the AKSZ construction
• A Lie Group Structure Underlying the Triplectic Geometry

Cited by in corpus (10)

• Double field theory algebroid and curved $L_{\infty }$-algebras
• Chiral approach to partially-massless fields
• Presymplectic gauge PDEs and Lagrangian BV formalism beyond jet-bundles
• Topological Dirac Sigma Models and the Classical Master Equation
• Geometric BV for twisted Courant sigma models and the BRST power finesse
• Basic curvature and the Atiyah cocycle in gauge theory
• Massless chiral fields in six dimensions
• Homotopy Manin Theories: Generalising Third-Way, Yang-Mills and Integrable Sigma Models
• Gravity from AKSZ-Manin theories in two, three, and four dimensions
• Consistent deformations in the presymplectic BV-AKSZ approach