Making Sense of Singular Gauge Transformations in 1+1 and 2+1 Fermion Models

We study the problem of decoupling fermion fields in 1+1 and 2+1 dimensions, in interaction with a gauge field, by performing local transformations of the fermions in the functional integral. This could always be done if singular (large) gauge transformations were allowed, since any gauge field configuration may be represented as a singular pure gauge field. However, the effect of a singular gauge transformation of the fermions is equivalent to the one of a regular transformation with a non-trivial action on the spinorial indices. For example, in the two dimensional case, singular gauge transformations lead naturally to chiral transformations, and hence to the usual decoupling mechanism based on Fujikawa Jacobians. In 2+1 dimensions, using the same procedure, different transformations emerge, which also give rise to Fujikawa Jacobians. We apply this idea to obtain the v.e.v of the fermionic current in a background field, in terms of the Jacobian for an infinitesimal decoupling transformation, finding the parity violating result.Comment: 14 pages, Late

Bogomolny equations for vortices in the noncommutative torus

We derive Bogomolny-type equations for the Abelian Higgs model defined on the noncommutative torus and discuss its vortex like solutions. To this end, we carefully analyze how periodic boundary conditions have to be handled in noncommutative space and discussed how vortex solutions are constructed. We also consider the extension to an $U(2)\times U(1)$ model, a simplified prototype of the noncommutative standard model.Comment: 23 pages, no figure

Vortex solutions in the noncommutative torus

Vortex configurations in the two-dimensional torus are considered in noncommutative space. We analyze the BPS equations of the Abelian Higgs model. Numerical solutions are constructed for the self-dual and anti-self dual cases by extending an algorithm originally developed for ordinary commutative space. We work within the Fock space approach to noncommutative theories and the Moyal-Weyl connection is used in the final stage to express the solutions in configuration space.Comment: 18 pages, 5 figure

Uniqueness of Bogomol'nyi equations and Born-Infeld like supersymmetric theories

We discuss Bogomol'nyi equations for general gauge theories (depending on the two Maxwell invariants $F^{\mu \nu} F_{\mu \nu}$ and $\tilde F^{\mu \nu} F_{\mu \nu}$) coupled to Higgs scalars. By analysing their supersymmetric extension, we explicitly show why the resulting BPS structure is insensitive to the particular form of the gauge Lagrangian: Maxwell, Born-Infeld or more complicated non-polynomial Lagrangians all satisfy the same Bogomol'nyi equations and bounds which are dictated by the underlying supersymmetry algebra.Comment: 10 pages, Late

Monopole Solutions in AdS Space

We find monopole solutions for a spontaneously broken SU(2)-Higgs system coupled to gravity in asymptotically anti-de Sitter space. We present new analytic and numerical results discussing,in particular, how the gravitational instability of self-gravitating monopoles depends on the value of the cosmological constant.Comment: 14 pages, 4 figures, Latex fil

Finite temperature regularization

We present a non-perturbative regularization scheme for Quantum Field Theories which amounts to an embedding of the originally unregularized theory into a spacetime with an extra compactified dimensions of length L ~ Lambda^{-1} (with Lambda an ultraviolet cutoff), plus a doubling in the number of fields, which satisfy different periodicity conditions and have opposite Grassmann parity. The resulting regularized action may be interpreted, for the fermionic case, as corresponding to a finite-temperature theory with a supersymmetry, which is broken because of the boundary conditions. We test our proposal in a perturbative calculation (the vacuum polarization graph for a D-dimensional fermionic theory) and in a non-perturbative one (the chiral anomaly).Comment: 17 pages, LaTeX fil

Non-Abelian Vortices on the Torus

We study periodic arrays of non-Abelian vortices in an $SU(N) \times U(1)$ gauge theory with $N_f$ flavors of fundamental matter multiplets. We carefully discuss the corresponding twisted boundary conditions on the torus and propose an ansatz to solve the first order Bogomolnyi equations which we find by looking to a bound of the energy. We solve the equations numerically and construct explicit vortex solutions

Parity Violation in the Three Dimensional Thirring Model

We discuss parity violation in the 3-dimensional (N flavour) Thirring model. We find that the ground state fermion current in a background gauge field does not posses a well defined parity transformation. We also investigate the connection between parity violation and fermion mass generation, proving that radiative corrections force the fermions to be massive.Comment: 11 page

On three dimensional bosonization

We discuss Abelian and non-Abelian three dimensional bosonization within the path-integral framework. We present a systematic approach leading to the construction of the bosonic action which, together with the bosonization recipe for fermion currents, describes the original fermion system in terms of vector bosons.Comment: 15 pages, LaTe

Supersymmetric Non-Abelian Born-Infeld Theory

Using the natural curvature invariants as building blocks in a superfield construction, we show that the use of a symmetric trace is mandatory if one is to reproduce the square root structure of the non-Abelian Dirac-Born-Infeld Lagrangian in the bosonic sector. We also discuss the BPS relations in connection with our supersymmetry construction.Comment: 13 pages, Latex, no figure