Local BRST cohomology in gauge theories

2000/02/29 by Glenn Barnich, Friedemann Brandt, Marc Henneaux · 24 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #hep-ph #hep-th

paper · pdf · doi:10.1016/s0370-1573(00)00049-1

published as Phys.Rept.338:439-569,2000 · 150 pages Latex file, minimal corrections, final version

crossref issued 2000/11/01 · crossref published 2000/11/01 · crossref published-print 2000/11/01 · openalex publication_date 2000/11/01 · arxiv created 2000/11/13 · crossref created 2002/07/25 · arxiv updated 2010/11/15 · crossref deposited 2021/05/03 · openalex created_date 2025/10/10 · crossref indexed 2026/07/15 · openalex updated_date 2026/07/28

Abstract

The general solution of the anomaly consistency condition (Wess-Zumino equation) has been found recently for Yang-Mills gauge theory. The general form of the counterterms arising in the renormalization of gauge invariant operators (Kluberg-Stern and Zuber conjecture) and in gauge theories of the Yang-Mills type with non power counting renormalizable couplings has also been worked out in any number of spacetime dimensions. This Physics Report is devoted to reviewing in a self-contained manner these results and their proofs. This involves computing cohomology groups of the differential introduced by Becchi, Rouet, Stora and Tyutin, with the sources of the BRST variations of the fields ("antifields") included in the problem. Applications of this computation to other physical questions (classical deformations of the action, conservation laws) are also considered. The general algebraic techniques developed in the Report can be applied to other gauge theories, for which relevant references are given.

Citations

• Quantization of Gauge Systems
• Local BRST cohomology for p-form gauge theories
• Effective Field Theories
• Ward identities in gauge theories
• Infinitesimal computations in topology
• Local BRST cohomology in the antifield formalism: I. General theorems
• Effective Field Theory and the Fermi Surface
• Anomalous Ward Identities in Spinor Field Theories
• Conservation of Isotopic Spin and Isotopic Gauge Invariance
• Effective Field Theories
• Phenomenological Lagrangians

Cited by

• Remarks on the BRST cohomology of supersymmetric gauge theories
• Four-dimensional couplings among BF and massless Rarita–Schwinger theories: a BRST cohomological approach
• The KT-BRST Complex of a Degenerate Lagrangian System
• REMOVAL OF VIOLATIONS OF THE MASTER WARD IDENTITY IN PERTURBATIVE QFT
• Interactions for a collection of spin-two fields intermediated by a massless p-form
• Lagrangian symmetries and supersymmetries depending on derivatives. Global analysis
• Local symmetries of the non-Abelian two-form
• The Wess Zumino consistency condition: a paradigm in renormalized perturbation theory
• On ghost condensation, mass generation and Abelian dominance in the maximal Abelian gauge
• Parent Field Theory and Unfolding in BRST First-Quantized Terms
• Algebroid Yang-Mills Theories
• Parity violating spin-two gauge theories
• On the generalized Freedman-Townsend model
• Anomaly freedom in Seiberg-Witten noncommutative gauge theories
• N=2 SUPER-YANG–MILLS ACTION AND BRST COHOMOLOGY
• Worldvolume supersymmetries for branes in plane waves
• Dynamical gluon mass generation from in linear covariant gauges
• Edge modes without edge modes
• Observables in topological Yang-Mills theorieswith extended shift supersymmetry
• Weak Power-Counting Theorem for the Renormalization of the Nonlinear Sigma Model in Four Dimensions
• The algebra of physical observables in non-linearly realized gauge theories
• Parent formulations, frame-like Lagrangians, and generalized auxiliary fields
• Quantum metamorphosis of conformal symmetry in N=4 super Yang–Mills theory
• Marc Henneaux [wikipedia]