Alberto Blasi

Infrared and ultraviolet finiteness of topological BF theory in two dimensions

The two-dimensional topological BF model is considered in the Landau gauge in the framework of perturbation theory. Due to the singular behaviour of the ghost propagator at long distances, a mass term to the ghost fields is introduced as an infrared regulator. Relying on the supersymmetric algebraic structure of the resulting massive theory, the authors study the infrared and ultraviolet renormalizability of the model, with the outcome that it is perturbatively finite.

Perturbative beta function of N = 2 super Yang-Mills theories

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 phi^2, phi(x) being the scalar field of the N=2 vector gauge multiplet. The nonrenormalization theorem for the beta function follows from the vanishing of the anomalous dimension of Tr phi^2.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 phi^2, phi(x) being the scalar field of the N=2 vector gauge multiplet. The nonrenormalization theorem for the beta function follows from the vanishing of the anomalous dimension of Tr phi^2.

Renormalizability of nonrenormalizable field theories

UERJ, Universidade do Estado do Rio de Janeiro, Departamento de Fi ´sica Teorica, Rua Sa˜o Francisco Xavier, 524, 20550-013,Maracana˜, Rio de Janeiro, Brazil~Received 8 December 1998; published 3 May 1999!We give a simple proof of the equivalence theorem, stating that two field theories related by nonlinear fieldtransformations have the same S matrix. We are thus able to identify a subclass of nonrenormalizable fieldtheories which are actually physically equivalent to renormalizable ones. Our strategy is to show by means ofthe Becchi-Rouet-Stora formalism that the ‘‘nonrenormalizable’’ part of such fake nonrenormalizable theoriesis a kind of gauge fixing, being confined in the cohomologically trivial sector of the theory.@S0556-2821~99!50112-4#PACS number~s!: 11.10.Gh

INFRARED REGULARIZATION OF YANG-MILLS THEORIES

We introduce an infrared regulator in Yang-Mills theories under the form of a mass term for the non-Abelian fields. We show that the resulting action, built in a covariant linear gauge, is multiplicatively renormalizable by proving the validity at all orders of the Slavnov identity defining the theory.

Maxwell?Chern?Simons theory with a boundary

The Maxwell?Chern?Simons (MCS) theory with a planar boundary is considered. The boundary is introduced according to Symanziks basic principles of locality and separability. A method of investigation is proposed, which, avoiding the straight computation of correlators, is appealing for situations where the computation of propagators, modified by the boundary, becomes quite complex. For the MCS theory, the outcome is that a unique solution exists, in the form of chiral conserved currents, satisfying a Ka??Moody algebra, whose central charge does not depend on the Maxwell term.

Duality and dimensional reduction of 5D BF theory

A planar boundary introduced à la Symanzik in the 5D topological BF theory, with only the requirements of locality and power counting, allows to uniquely determine a gauge invariant, non-topological 4D Lagrangian. The boundary condition on the bulk fields is interpreted as a duality relation for the boundary fields, in analogy with the fermionization duality which holds in the 3D case. This suggests that the 4D degrees of freedom might be fermionic, although starting from a bosonic bulk theory. The method we propose to dimensionally reduce a Quantum Field Theory and to identify the resulting degrees of freedom can be applied to a generic spacetime dimension.

Nonrenormalization properties of the Chern-Simons action coupled to matter

Abstract We analyze an abelian gauge model in three dimensions which includes massless scalar matter fields. By controlling the trace anomalies with a local dilatation Ward identity, we show that, in perturbation theory and within the BPHZL scheme, the Chern-Simons term has no radiative corrections. This implies, in particular, the vanishing of the corresponding β function in the renormalization group equation.

Symanzik's method applied to fractional quantum Hall edge states

The method of separability, introduced by Symanzik, is applied in order to describe the effect of a boundary for a fractional quantum Hall liquid in the Laughlin series. An Abelian Chern-Simons theory with plane boundary is considered and the Green functions both in the bulk and on the edge are constructed, following a rigorous, perturbative, quantum field theory treatment. We show that the conserved boundary currents find an explicit interpretation in terms of the continuity equation with the electron density satisfying the Tomonaga-Luttinger commutation relation.

Noncommutative two-dimensional BF model

We consider the noncommutative extension of the BF theory in two spacetime dimensions. We show that the introduction of the noncommutative parameter θµν , already at first order in the analytical sector, induces infinitely many terms in the quantum extension of the model. This clashes with the commonly accepted rules of QFT, and we believe that this problem is not peculiar to this particular model, but it might concern the noncommutative extension of any ordinary quantum field theory obtained via the Moyal prescription. A detailed study of noncommutative anomalies is also presented.

INSTABILITIES OF NONCOMMUTATIVE TWO-DIMENSIONAL BF MODEL

The noncommutative extension of two-dimensional BF model is considered. It is shown that the realization of the noncommutative map via the Groenewold–Moyal star product leads to instabilities of the action, hence to a non-renormalizable theory.