Seiberg-Witten maps and anomalies in noncommutative Yang-Mills theories

A BRST-cohomological analysis of Seiberg-Witten maps and results on gauge anomalies in noncommutative Yang-Mills theories with general gauge groups are reviewed.Comment: 9 pages, talk at 9th Adriatic Meeting, Dubrovnik, Croatia, 4-14 Sept. 200

Uniqueness of the Freedman-Townsend Interaction Vertex For Two-Form Gauge Fields

Let $B_{\mu \nu }^a$ ($a=1,...,N$) be a system of $N$ free two-form gauge fields, with field strengths $H_{\mu \nu \rho }^a = 3 \partial _{[\mu }B_{\nu \rho ]}^a$ and free action $S_0$ equal to $(-1/12)\int d^nx\ g_{ab}H_{\mu \nu \rho }^aH^{b\mu \nu \rho }$ ($n\geq 4$). It is shown that in $n>4$ dimensions, the only consistent local interactions that can be added to the free action are given by functions of the field strength components and their derivatives (and the Chern-Simons forms in $5$ mod $3$ dimensions). These interactions do not modify the gauge invariance $B_{\mu \nu }^a\rightarrow B_{\mu \nu }^a+\partial _{[\mu }\Lambda _{\nu ]}$ of the free theory. By contrast, there exist in $n=4$ dimensions consistent interactions that deform the gauge symmetry of the free theory in a non trivial way. These consistent interactions are uniquely given by the well-known Freedman-Townsend vertex. The method of proof uses the cohomological techniques developed recently in the Yang-Mills context to establish theorems on the structure of renormalized gauge-invariant operators.Comment: 12 pages Latex fil

Background charges and consistent continuous deformations of 2d2d gravity theories

We construct and discuss all background charges and continuous consistent deformations of standard $2d$ gravity theories with scalar matter fields. It turns out that the background charges and those deformations which change nontrivially both the form of the action and of its gauge symmetries are closely linked and exist only if the target space has at least one special (`covariantly constant') Killing vector which must be a null vector in the case of the deformations. The deformed actions provide interesting novel $2d$ gravity models. We argue that some of them lead to non-critical string theories.Comment: 9 pages, LaTeX. Changes in the discussion on the Liouville fiel

Refining the anomaly consistency condition

In the extended antifield formalism, a quantum BRST differential for anomalous gauge theories is constructed. Local BRST cohomological classes are characterized, besides the form degree and the ghost number, by the length of their descents and of their lifts, and this both in the standard and the extended antifield formalism. It is shown that during the BRST invariant renormalization of a local BRST cohomological class, the anomaly that can appear is constrained to be a local BRST cohomological class with a shorter descent and a longer lift than the given class. As an application of both results, a simple approach to the Adler-Bardeen theorem for the non abelian gauge anomaly is proposed. It applies independently of the gauge fixing, of power counting restrictions and does not rely on the use of the Callan-Symanzik equation.Comment: 20 pages RevTex fil

Boundary charges in gauge theories: using Stokes theorem in the bulk

Boundary charges in gauge theories (like the ADM mass in general relativity) can be understood as integrals of linear conserved n-2 forms of the free theory obtained by linearization around the background. These forms are associated one-to-one to reducibility parameters of this background (like the time-like Killing vector of Minkowski space-time). In this paper, closed n-2 forms in the full interacting theory are constructed in terms of a one parameter family of solutions to the full equations of motion that admits a reducibility parameter. These forms thus allow one to apply Stokes theorem without bulk contributions and, provided appropriate fall-off conditions are satisfied, they reduce asymptotically near the boundary to the conserved n-2 forms of the linearized theory. As an application, the first law of black hole mechanics in asymptotically anti-de Sitter space-times is derived.Comment: 17 pages Latex file, improved presentation, main results unchanged, additional section on first law, additional reference

A note on the BRST cohomology of the extended antifield formalism

The relevance of the BRST cohomology of the extended antifield formalism is briefly discussed along with standard homological tools needed for its computation.Comment: 10 pages Latex file, Proceedings of the spring school "Q.F.T., Supersymmetry and Superstrings" in Calimanesti, Romania, April 199

BRST analysis of general mechanical systems

We study the groups of local BRST cohomology associated to the general systems of ordinary differential equations, not necessarily Lagrangian or Hamiltonian. Starting with the involutive normal form of the equations, we explicitly compute certain cohomology groups having clear physical meaning. These include the groups of global symmetries, conservation laws and Lagrange structures. It is shown that the space of integrable Lagrange structures is naturally isomorphic to the space of weak Poisson brackets. The last fact allows one to establish a direct link between the path-integral quantization of general not necessarily variational dynamics by means of Lagrange structures and the deformation quantization of weak Poisson brackets.Comment: 38 pages, misprints corrected, references and the Conclusion adde

Black hole entropy from non-proper gauge degrees of freedom: II. The charged vacuum capacitor

The question which degrees of freedom are responsible for the classical part of the Gibbons-Hawking entropy is addressed. A physical toy model sharing the same properties from the viewpoint of the linearized theory is a charged vacuum capacitor. In Maxwell's theory, the gauge sector including ghosts is a topological field theory. When computing the grand canonical partition function with a chemical potential for electric charge in the indefinite metric Hilbert space of the BRST quantized theory, the classical contribution originates from the part of the gauge sector that is no longer trivial due to the boundary conditions required by the physical set-up. More concretely, in the benchmark problem of a planar charged vacuum capacitor, we identify the degrees of freedom that, in the quantum theory, give rise to an additional contribution to the standard black body result proportional to the area of the plates, and that allow for a microscopic derivation of the thermodynamics of the charged capacitor.Comment: 27 pages, V2: improved discussion of thermodynamics in section 2, references added, no other change

A general non renormalization theorem in the extended antifield formalism

In the context of algebraic renormalization, the extended antifield formalism is used to derive the general forms of the anomaly consistency condition and of the Callan-Symanzik equation for generic gauge theories. A local version of the latter is used to derive sufficient conditions for the vanishing of beta functions associated to terms whose integrands are invariant only up to a divergence for an arbitrary non trivial non anomalous symmetry of the Lagrangian. These conditions are independent of power counting restrictions and of the form of the gauge fixation.Comment: 25 pages Latex file, major revision and extensio

Higher order cohomological restrictions on anomalies and counterterms

Using a regularization with the properties of dimensional regularization, higher order local consistency conditions on one loop anomalies and divergent counterterms are given. They are derived without any a priori assumption on the form of the BRST cohomology and can be summarized by the statements that (i) the antibracket involving the first order divergent counterterms, respectively the first order anomaly, with any BRST cocycle is BRST exact, (ii) the first order divergent counterterms can be completed into a local deformation of the solution of the master equation and (iii) the first order anomaly can be deformed into a local cocycle of the deformed solution.Comment: 11 pages Latex file, mistake in assumption 2 forces a version limited to one loop considerations with a different derivation of main result