F.A. Schaposnik

Chiral symmetry and functional integral

Abstract The change in the fermionic functional integral measure under chiral rotations is analyzed. Using the ζ-function method, the evaluation of chiral Jacobians to theories including nonhermitian Dirac operators D , can be extended in a natural way. (This being of interest, for example, in connection with the Weinberg-Salam model or with the relativistic string theory.) Results are compared with those obtained following other approaches, the possible discrepancies are analyzed and the equivalence of the different methods under certain conditions on D is proved. Also shown is how to compute the Jacobian for the case of a finite chiral transformation and this result is used to develop a sort of path-integral version of bosonization in d = 2 space-time dimensions. This result is used to solve in a very simple and economical way relevant d = 2 fermionic models. Furthermore, some interesting features in connection with the θ-vacuum in d = 2,4 gauge theories are discussed.

Path Integral Formulation of Two-dimensional Gauge Theories With Massless Fermions

Abstract We study (1 + 1) dimensional gauge theories [with SU( N ) and diagonal SU( N ) color symmetry] using the functional integral method. We construct an effective lagrangian by performing a change in the fermionic variables, and then investigate relevant phenomena such as the intrinsic Higgs mechanism and color screening.

Wess-Zumino-Witten and fermion models in noncommutative space

Abstract We analyze the connection between Wess–Zumino–Witten and free fermion models in two-dimensional noncommutative space. Starting from the computation of the determinant of the Dirac operator in a gauge field background, we derive the corresponding bosonization recipe studying, as an example, bosonization of the U(N) Thirring model. Concerning the properties of the noncommutative Wess–Zumino–Witten model, we construct an orbit-preserving transformation that maps the standard commutative WZW action into the noncommutative one.

Chern-Simons formulation of noncommutative gravity in three dimensions

We formulate noncommutative three-dimensional (3d) gravity by making use of its connection with 3d Chern-Simons theory. In the Euclidean sector, we consider the particular example of topology T 2 ×R and show that the 3d black hole solves the noncommutative equations. We then consider the black hole on a constant U(1) background and show that the black hole charges (mass and angular momentum) are modified by the presence of this background. CONICET Associated with CICBA

A comment on bosonization in d ≥ 2 dimensions

Abstract We discuss recent results on bosonization in d ≥ 2 space-time dimensions by giving a very simple derivation for the bosonic representation of the original free fermionic model both in the abelian and non-abelian cases. We carefully analyse the issue of symmetries in the resulting bosonic model as well as the recipes for bosonization of fermion currents.

Monopole solutions in AdS space

Abstract 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.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.

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.Abstract 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.

ζ‐function method and the evaluation of fermion currents

Using the ζ‐function method, a prescription for the evaluation of fermion currents in the presence of background fields is given. The method preserves gauge invariance at each step of the computation and yields to a finite answer showing the relevant physical properties for arbitrary background configurations. Examples for n=2,3 dimensions are worked out, emphasizing the connection between preservation of gauge invariance and violation of other symmetries (chiral symmetry for n=2, parity for n=3).

Non-Abelian vortices in Chern-Simons theories and their induced effective theory

Non-Abelian vortices for a supersymmetric N = 2 Chern-Simons-Higgs theory are explicitly constructed. We introduce N Higgs fields in the fundamental representation of the U(N) gauge group in order to have a color-flavor SU(N) group remaining unbroken in the asymmetric phase. Bogomol’nyi-like first order equations are found and rotationally symmetric solutions are proposed. These solutions are shown to be truly non-Abelian by parameterizing them in terms of orientational collective coordinates. The low energy effective action for the orientational moduli results to be the one-dimensional supersymmetricN = 2 CP N 1 model. We analyze the quantum mechanics of this effective theory in the N = 2 case. PACS numbers:

THE ζ FUNCTION ANSWER TO PARITY VIOLATION IN THREE-DIMENSIONAL GAUGE THEORIES

We study parity violation in (2+1)-dimensional gauge theories coupled to massive fermions. Using the ζ function regularization approach we evaluate the ground state fermion current in an arbitrary gauge field background, showing that it gets two different contributions which violate parity invariance and induce a Chern–Simons term in the gauge field effective action. One is related to the well-known classical parity breaking produced by a fermion mass term in three dimensions; the other, already present for massless fermions, is related to peculiarities of gauge-invariant regularization in odd-dimensional spaces.