Parent formulation at the Lagrangian level

Abstract

The recently proposed first-order parent formalism at the level of equations of motion is specialized to the case of Lagrangian systems. It is shown that for diffeomorphism-invariant theories the parent formulation takes the form of an AKSZ-type sigma model. The proposed formulation can be also seen as a Lagrangian version of the BV-BRST extension of the Vasiliev unfolded approach. We also discuss its possible interpretation as a multidimensional generalization of the Hamiltonian BFV--BRST formalism. The general construction is illustrated by examples of (parametrized) mechanics, relativistic particle, Yang--Mills theory, and gravity.

26 pages, discussion of the truncation extended, typos corrected, references added

References in corpus (26)

• Double Field Theory
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• The Geometry of the Master Equation and Topological Quantum Field Theory
• Local BRST cohomology in gauge theories
• A path integral approach to the Kontsevich quantization formula
• Background independent action for double field theory
• Consistent couplings between fields with a gauge freedom and deformations of the master equation
• Local BRST cohomology in the antifield formalism: I. General theorems
• Canonical Structure of Classical Field Theory in the Polymomentum Phase Space
• On the Frame-Like Formulation of Mixed-Symmetry Massless Fields in (A)dS(d)
• Local BRST cohomology in Einstein--Yang--Mills theory
• Parent field theory and unfolding in BRST first-quantized terms
• Local BRST cohomology and covariance
• Bosonic conformal higher--spin fields of any symmetry
• Lagrange structure and quantization
• Unified BRST description of AdS gauge fields
• Frame-like Actions for Massless Mixed-Symmetry Fields in Minkowski space
• Massless Poincare modules and gauge invariant equations
• Superfield BRST Charge and the Master Action
• Parent form for higher spin fields on anti-de Sitter space
• A Poincare lemma for sigma models of AKSZ type
• Two-column higher spin massless fields in AdS(d)
• First order parent formulation for generic gauge field theories
• Towards frame-like gauge invariant formulation for massive mixed symmetry bosonic fields. II. General Young tableau with two rows
• Generalized Poisson sigma models
• Finite dimensional AKSZ-BV theories

Cited by in corpus (21)

• Cubic Vertices for Symmetric Higher-Spin Gauge Fields in $(A)d{S}_d$
• Higher order singletons, partially massless fields and their boundary values in the ambient approach
• Higher-Spin Interactions: four-point functions and beyond
• Unified BRST approach to (partially) massless and massive AdS fields of arbitrary symmetry type
• On matter-free Higher Spin Gravities in 3d: (partially)-massless fields and general structure
• A minimal BV action for Vasiliev's four-dimensional higher spin gravity
• Parent formulations, frame-like Lagrangians, and generalized auxiliary fields
• Frame-like Lagrangians and presymplectic AKSZ-type sigma models
• Type-B Formal Higher Spin Gravity
• Notes on conformal invariance of gauge fields
• Gauge PDE and AKSZ-type Sigma Models
• Presymplectic AKSZ formulation of Einstein gravity
• Presymplectic BV-AKSZ formulation of Conformal Gravity
• General Relativity and the AKSZ construction
• BV equivalence with boundary
• Presymplectic gauge PDEs and Lagrangian BV formalism beyond jet-bundles
• Gravity with torsion as deformed $BF$ theory
• Symmetry breaking mechanisms of the 3BF action for the Standard Model coupled to gravity
• Gravity from AKSZ-Manin theories in two, three, and four dimensions
• Consistent deformations in the presymplectic BV-AKSZ approach
• Homotopy Manin Theories: Generalising Third-Way, Yang-Mills and Integrable Sigma Models