Fidel A. Schaposnik

The fermion-boson mapping in three-dimensional quantum field theory

Abstract We discuss bosonization in three dimensions by establishing a connection between the massive Thirring model and the Maxwell-Chern-Simons theory. We show, to lowest order in inverse fermion mass, the identity between the corresponding partition functions; from this, a bosonization identity for the fermion current, valid for length scales long compared with the Compton wavelength of the fermion, is inferred. We present a non-local operator in the Thirring model which exhibits fractional statistics.We discuss bosonization in three dimensions by establishing a connection between the massive Thirring model and the Maxwell-Chern-Simons theory. We show, to lowest order in inverse fermion mass, the identity between the corresponding partition functions; from this, a bosonization identity for the fermion current, valid for length scales long compared with the Compton wavelength of the fermion, is inferred. We present a non-local operator in the Thirring model which exhibits fractional statistics.

Supersymmetry and Bogomol'nyi equations in the Abelian Higgs model

Abstract The N = 2 supersymmetric extension of the 2+1 dimensional Abelian Higgs model is discussed. By analysing the resulting supercharge algebra, the connection between supersymmetry and Bogomolnyi equations is clarified. Analogous results are presented when the model is considered in 2 dimensional (Euclidean) space.

Bosonization of three-dimensional non-abelian fermion field theories

Abstract We discuss bosonization in three dimensions of an SU(N) massive Thirring model in the low-energy regime. We find that the bosonized theory is related (but not equal) to (SU(N)) Yang-Mills-Chern-Simons gauge theory. For free massive fermions bosonization leads, at low energies, to the pure SU(N) (level k = 1) Chern-Simons theory.

The Wess-Zumino-Witten term in non-commutative two-dimensional fermion models

We study the effective action associated to the Dirac operator in two dimensional non-commutative Field Theory. Starting from the axial anomaly, we compute the determinant of the Dirac operator and we find that even in the U(1) theory, a Wess-Zumino-Witten like term arises.

Supergravity and a Bogomol'nyi bound in three dimensions

Abstract We discuss the (2 + 1)-dimensional Abelian Higgs model coupled to N = 2 supergravity. The model provides an example on how unbroken supercharges can be defined, circumventing the problem of finding supercovariantly constant Killing spinors in 2+1 dimensions. We show that this is due to the existence of gravitating vortices saturating a Bogomolnyi bound. The corresponding self-duality equations imply, through an integrability condition, the Einstein equation.

Self-dual Chern-Simons solitons in noncommutative space

We construct exact soliton solutions to the Chern-Simons-Higgs system in non-commutative space, for non-relativistic and relativistic models. In both cases we find regular vortex-like solutions to the BPS equations which approach the ordinary selfdual non-topological and topological solitons when he non-commutative parameter θ goes to zero.

Monopole and dyon solutions in AdS space

Abstract We consider monopole and dyon classical solutions of the Yang-Mills-Higgs system coupled to gravity in asymptotically anti-de Sitter space. We discuss both singular and regular solutions to the second order equations of motion showing that singular Wu-Yang like dyons can be found, the resulting metric being of the Reissner-Nordstrom type (with cosmological constant). Concerning regular solutions, we analyze the conditions under which they can be constructed discussing, for vanishing coupling constant, the main distinctive features related to the anti-de Sitter asymptotic condition; in particular, we find in this case that the v.e.v. of the Higgs scalar, | H (∞)| , should be quantized in units of the natural mass scale 1/e r 0 (related to the cosmological constant) according to | H (∞)| 2 =m(m+1)(e r 0 ) −2 , with m ∈ Z .

Noncommutative Solitons and Instantons

I review different approaches to the construction of vortex and instanton solutions in noncommutative field theories.

On three dimensional bosonization

Abstract 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.

Renormalization group functions for the Wess-Zumino model: Up to 200 loops through Hopf algebras

Abstract We obtain the contributions to the renormalization group functions of all the diagrams containing the unique one-loop primitive divergence of a simple supersymmetric Wess–Zumino model, up to more than 200 loops. The asymptotic behavior of the coefficients in the expansion of the anomalous dimension is analysed.