A Poincaré Lemma for sigma models of AKSZ type

DOI10.1016/j.geomphys.2010.11.014zbMath1207.81148arXiv0905.0547OpenAlexW2099635623WikidataQ124830488 ScholiaQ124830488MaRDI QIDQ627214

Maxim Grigoriev, Glenn Barnich

Publication date: 21 February 2011

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.0547

zbMATH Keywords

variational principlestopological field theoriesLagrangian and Hamiltonian formalismgauge theories and BV quantizationsymmetries and conservation laws

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Yang-Mills and other gauge theories in quantum field theory (81T13) Topological field theories in quantum mechanics (81T45) Symplectic aspects of Floer homology and cohomology (53D40) Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems (70S05) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

Related Items

Homotopy Cartan calculus and inner deformations of \(A_{\infty}\)-algebras, <scp>A</scp> note on local BRST cohomology of Yang-Mills type theories with free Abelian factors, Characteristic cohomology and observables in higher spin gravity, BRST analysis of general mechanical systems, New conformal higher spin gravities in \(3d\), Presymplectic gauge PDEs and Lagrangian BV formalism beyond jet-bundles, Gauge PDE and AKSZ‐type Sigma Models, Minimal models of field theories: SDYM and SDGR, Minimal model of chiral higher spin gravity, Parent formulation at the Lagrangian level, Local BRST cohomology in (non-)Lagrangian field theory, ON LAGRANGE STRUCTURE OF UNFOLDED FIELD THEORY, Presymplectic AKSZ formulation of Einstein gravity, First order parent formulation for generic gauge field theories, A minimal BV action for Vasiliev's four-dimensional higher spin gravity, Parent formulations, frame-like Lagrangians, and generalized auxiliary fields, Chern-Simons action for inhomogeneous Virasoro group as extension of three dimensional flat gravity, Batalin-Vilkovisky formality for Chern-Simons theory, Rigid symmetries and conservation laws in non-Lagrangian field theory, Frame-like Lagrangians and presymplectic AKSZ-type sigma models

Cites Work

• Consistent equations for interacting gauge fields of all spins in \(3+1\) dimensions
• Quantization of Donaldson-Uhlenbeck-Yau theory
• Comments on the gauge fixed BRST cohomology and the quantum Noether method
• Homological perturbation theory and the algebraic structure of the antifield-antibracket formalism for gauge theories
• Finite-dimensional AKSZ-BV theories
• The \({\mathcal C}\)-spectral sequence, Lagrangian formalism, and conservation laws. I: The linear theory
• Spacetime locality of the BRST formalism
• Parent field theory and unfolding in BRST first-quantized terms
• B.R.S. algebras. Analysis of the consistency equations in gauge theory
• Consistent equations for interacting massless fields of all spins in the first order in curvatures
• Hamiltonian operators and algebraic structures related to them
• Semiclassical approximation in Batalin-Vilkovisky formalism
• Two-dimensional gravity and nonlinear gauge theory
• Nonlinear equations for symmetric massless higher spin fields in (A)dS\(_d\)
• The Wess-Zumino consistency condition for \(p\)-form gauge theories
• Local BRST cohomology in gauge theories
• A path integral approach to the Kontsevich quantization formula.
• On the quantum Batalin-Vilkovisky formalism and the renormalization of nonlinear symmetries.
• Covariant theory of asymptotic symmetries, conservation laws and central charges
• Hamiltonian BRST and Batalin-Vilkovisky formalisms for second quantization of gauge theories
• Existence, uniqueness and cohomology of the classical BRST charge with ghosts of ghosts
• On complexes related with calculus of variations
• Local BRST cohomology in Einstein-Yang-Mills theory
• Local BRST cohomology in the antifield formalism. I: General theorems
• Higher derived brackets and homotopy algebras
• POISSON STRUCTURE INDUCED (TOPOLOGICAL) FIELD THEORIES
• The Geometry of the Master Equation and Topological Quantum Field Theory
• BRST quantization of quasisymplectic manifolds and beyond
• Higher Poisson Brackets and Differential Forms
• Isomorphisms between the Batalin–Vilkovisky antibracket and the Poisson bracket
• Becchi–Rouet–Stora cohomology of zero curvature systems. I. The complete ladder case
• Algebraic Renormalization
• Cohomological analysis of gauge-fixed gauge theories
• Generalized Poisson sigma models
• Quantization of relativistic systems with constraints
• On the AKSZ formulation of the Poisson sigma model.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item