Presymplectic BV-AKSZ formulation of Conformal Gravity

Abstract

We elaborate on the presymplectic BV-AKSZ approach to local gauge theories and apply it to conformal gravity. More specifically, we identify a compatible presymplectic structure on the minimal model of the total BRST complex of this theory and show that together with the BRST differential it determines a full-scale BV formulation for a specific frame-like action which seems to be previously unknown. Remarkably, the underlying frame-like description requires no artificial off-shell constraints. Instead, the action becomes equivalent to the usual conformal gravity one, upon gauging away all the variables belonging to the kernel of the presymplectic structure. Finally, we show how the presymplectic BV-AKSZ approach extends to generic gauge theories.

arXiv comment31 pages + appendix

References in corpus (39)

• The Geometry of the Master Equation and Topological Quantum Field Theory
• Local BRST cohomology in gauge theories
• Local BRST cohomology in the antifield formalism: I. General theorems
• Making the Case for Conformal Gravity
• Conformal Supergravity in Twistor-String Theory
• The self-dual sector of QCD amplitudes
• Conformal Higher Spin Theory
• Effective action in a higher-spin background
• Geometry of jet spaces and integrable systems
• Higher order singletons, partially massless fields and their boundary values in the ambient approach
• On limits of superstring in AdS_5 x S^5
• Local BRST cohomology in Einstein--Yang--Mills theory
• Parent field theory and unfolding in BRST first-quantized terms
• Local BRST cohomology and covariance
• Partition function of free conformal higher spin theory
• Actions for Self-dual Higher Spin Gravities
• Algebraic Classification of Weyl Anomalies in Arbitrary Dimensions
• Superfield BRST Charge and the Master Action
• On matter-free Higher Spin Gravities in 3d: (partially)-massless fields and general structure
• General solutions of the Wess-Zumino consistency condition for the Weyl anomalies
• First order parent formulation for generic gauge field theories
• Conformal higher spin scattering amplitudes from twistor space
• Parent formulations, frame-like Lagrangians, and generalized auxiliary fields
• Conformal Field Theory in Conformal Space
• Spontaneous breaking of conformal invariance in theories of conformally coupled matter and Weyl gravity
• Frame-like Lagrangians and presymplectic AKSZ-type sigma models
• Superfield Quantization
• A Weyl-covariant tensor calculus
• Parent formulation at the Lagrangian level
• Conformal geometry and (super)conformal higher-spin gauge theories
• Conformal Higher Spin Theory and Twistor Space Actions
• Superfield Formulation of the Phase Space Path Integral
• On conformal higher spins in curved background
• Presymplectic structures and intrinsic Lagrangians for massive fields
• Seiberg-Witten maps in the context of the antifield formalism
• Higher Spin Gravities and Presymplectic AKSZ Models
• Presymplectic current and the inverse problem of the calculus of variations
• Introduction to Quantization of Conformal Gravity
• Unfolding Conformal Geometry

Cited by in corpus (5)

• Chiral approach to partially-massless fields
• Presymplectic gauge PDEs and Lagrangian BV formalism beyond jet-bundles
• Model-independent Gamma-Ray Bursts Constraints on Cosmological Models Using Machine Learning
• Dynamical Implementation of the Constraints in Conformal Gravity
• Consistent deformations in the presymplectic BV-AKSZ approach