Local BRST cohomology in gauge theories

By G. Barnich, Friedemann Brandt, M. Henneaux. Physics reports, 2000

536 citations recorded by the source corpus.

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 space–time 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.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/759df5f961996e32c89b0a20925320f26d4e761a

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Citations in the corpus

Boundary charges in gauge theories: using Stokes theorem in the bulk (2003, background): “Recent results from variational calculus [6] (see [7] for a review and also [8, 9]) corroborate this point of view: • when restricted to solutions of the equations of motion, equivalence classes of closed, local, n − 2 forms up to exact, local, n − 2 forms correspond one-to-one to nontrivial reducib”
Chiral gravity, log gravity, and extremal CFT (2009, methodology): “Our expression follows from the covariant formalism [37, 38], which is based on [39] and has been developed in great detail for a wide variety of applications in [40].”
Kerr/CFT Correspondence (2008, background): “ metric are not subleading, the charges can have nonlinear corrections, which must be carefully considered. For this purpose the covariant formalism of Barnich, Brandt and Comp`ere [34, 35], based on [36, 37, 38, 39, 40, 41] and further developed in [42, 43], is the most complete and will be adopted”
Batalin-Vilkovisky Formalism in Perturbative Algebraic Quantum Field Theory (2011, background): “Results in this direction were obtained in [3,4,6].”
Advanced Lectures on General Relativity (2018, methodology): “The cohomological formalism for defining the surface charges (and in particular the proof of uniqueness or “Generalized Noether theorem") was developed in [3, 17, 7].”
Renormalized Quantum Yang-Mills Fields in Curved Spacetime (2007, unknown): “ructed out of the ﬁelds. The algebraic Poincare lemmahas been rediscoveredmany times,and different proofs exist in the literature. Here we follow the proof given in [113], for other accounts see e.g. [5]. Proof: One ﬁrst considers the case when α[Φ,Ψ]is linear in Ψ, i.e., of the form αµ1...µp = k ∑ ”
On the uniqueness of higher-spin symmetries in AdS and CFT (2013, methodology): “e system with open algebra10 for which the Batalin-Vilkovisky formalism [48] is particularly useful. However, we refrain from resorting to the antiﬁeld formalism here and refer to the book and review [49,50] for information and references. Perturbativedeformations. Using De Witt’s condensed notation”
Covariant theory of asymptotic symmetries, conservation laws and central charges (2001, methodology): “The left hand sides of the (Euler-Lagrange) equations of motion of the full and the free theory and their total derivatives, ∂(μ)δL/δφ i and ∂(μ)δL /δφ, have been assumed to satisfy important regularity conditions described for instance in [47, 48] and spelled out in detail in the context of Yang-Mi”
L∞‐Algebras of Classical Field Theories and the Batalin–Vilkovisky Formalism (2018, methodology): “For more detailed reviews, we refer the reader to Section 8 of [58] as well as the papers [59–63] and [64–66].”