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.

notations updated, typos corrected, 23 pages

References in corpus (7)

• Edge modes of gravity -- II: Corner metric and Lorentz charges
• Edge modes of gravity. Part III. Corner simplicity constraints
• First order parent formulation for generic gauge field theories
• Parent formulations, frame-like Lagrangians, and generalized auxiliary fields
• Parent formulation at the Lagrangian level
• Asymptotic symmetries in the BV-BFV formalism
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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