We consider a model which effectively restricts the functional integral of Yang-Mills theories to the fundamental modular region. Using algebraic arguments, we prove that this theory has the same divergences as ordinary Yang Mills theory in the Landau gauge and that it is unitary. The restriction of the functional integral is interpreted as a kind of spontaneous breakdown of the BRS symmetry.

The complete renormalization procedure of a general N = 1 supersymmetric gauge theory in the Wess-Zumino gauge is presented, using the regulator free "algebraic renormalization" procedure. Both gauge invariance and supersymmetry are included into one single BRS invariance. The form of the general nonabelian anomaly is given. Furthermore, it is explained how the gauge BRS and the supersymmetry functional operators can be extracted from the general BRS operator. It is then shown that the supersymmetry operators actually belong to the closed, finite, Wess-Zumino superalgebra when their action is restricted to the space of the "gauge invariant operators", i.e. to the cohomology classes of the gauge BRS operator.

We provide an analytical derivation of the thermoelectric transport coefficients of the simplest momentum-dissipating model in gauge/gravity where the lack of momentum conservation is realized by means of explicit graviton mass in the bulk. We rely on the procedure recently described by Donos and Gauntlett for holographic models where momentum dissipation is realized through nontrivial scalars. The analytical approach confirms and supports the results found previously by means of numerical computations and the associated holographic renormalization procedure. Importantly, it also provides a precise identification of the range of validity of the hydrodynamic approximation.

We present a systematic definition and analysis of the thermo-electric linear response in gauge/gravity systems focusing especially on models with massive gravity in the bulk and therefore momentum dissipation in the dual field theory. A precise treatment of finite counter-terms proves to be essential to yield a consistent physical picture whose hydrodynamic and beyond-hydrodynamics behaviors noticeably match with field theoretical expectations. The model furnishes a possible gauge/gravity description of the crossover from the quantum-critical to the disorder-dominated Fermi-liquid behaviors, as expected in graphene.

Antisymmetric tensor fields are discussed. The model, as other topological field theories, possesses a supersymmetric off-shell structure which can be used to define a class of Slavnov invariant observables

We provide N = 1 Super Yang-Mills theory in the Wess-Zumino gauge with mass terms for the supersymmetric partners of the gauge fields and of the matter fields, together with a supersymmetric mass term for the fermionic matter fields. All mass terms are chosen in such a way to induce soft supersymmetry breakings at most, while preserving gauge invariance to all orders of perturbation theory. The breakings are controlled through an extended Slavnov-Taylor identity. The renormalization analysis, both in the ultraviolet and in the infrared region, is performed.

We study the algebraic renormalization of N = 2 Supersymmetric Yang-Mills theories coupled to matter. A regularization procedure preserving both the BRS invariance and the supersymmetry is not known yet, therefore it is necessary to adopt the algebraic method of renormalization, which does not rely on any regularization scheme. The whole analysis is reduced to the solution of cohomology problems arising from the generalized Slavnov operator which summarizes all the symmetries of the model. Besides to unphysical renormalizations of the quantum fields, we find that the only coupling constant of N = 2 SYMs can get quantum corrections. Moreover we prove that all the symmetries defining the theory are algebraically anomaly-free.hep-th/9501057

An algebraic proof of the nonrenormalization theorem for the perturbative beta function of the coupling constant of N = 2 Super Yang-Mills theory is provided. The proof relies on a fundamental relationship between the N = 2 Yang-Mills action and the local gauge invariant polynomial Tr φ 2 , φ(x) being the scalar field of the N = 2 vector gauge multiplet. The nonrenormalization theorem for the β g function follows from the vanishing of the anomalous dimension of Tr φ 2 .