Wifredo García Fuertes

On the solitons of the Chern-Simons-Higgs model

Abstract. Several issues concerning the self-dual solutions of the Chern-Simons-Higgs model are addressed. The topology of the configuration space of the model is analysed when the space manifold is either the plane or an infinite cylinder. We study the local structure of the moduli space of self-dual solitons in the second case by means of an index computation. It is shown how to manage the non-integer contribution to the heat-kernel supertrace due to the non-compactness of the base space. A physical picture of the local coordinates parametrizing the non-topological soliton moduli space arises.

A note on dual superconductivity and confinement

Abstract Electric self-dual vortices arising as BPS states in the strong coupling limit of N =2 supersymmetric Yang-Mills theory, softly broken to N =1, are reported.

On an approach for computing the generating functions of the characters of simple Lie algebras

We describe a general approach to obtain the generating functions of the characters of simple Lie algebras which is based on the theory of the quantum trigonometric Calogero–Sutherland model. We show how the method works in practice by means of a few examples involving some low rank classical algebras.

Self-dual solitons in N=2 supersymmetric Chern-Simons gauge theory

The low energy effective theory of planar QED with a non-local four-fermion interaction including Gross–Neveu and Thirring terms is shown to be equivalent to a Chern–Simons–Higgs model of special characteristics. We study the restrictions imposed by self-duality and supersymmetry, finding in both cases a plethora of (some new) topological and non-topological solitons. The non-relativistic limit of our model generalizes the effective Ginzburg–Landau theory for the fractional quantum Hall effect such that our solitons would be the relativistic version of quasi-particle and quasi-hole excitations.

Generating functions and multiplicity formulas: The case of rank two simple Lie algebras

A procedure is described that makes use of the generating function of characters to obtain a new generating function H giving the multiplicities of each weight in all the representations of a simple Lie algebra. The way to extract from H explicit multiplicity formulas for particular weights is explained and the results corresponding to rank two simple Lie algebras are shown.

Semilocal Chern–Simons defects

We find both radially symmetric and more general solutions in a Chern–Simons–Higgs model with a Higgs doublet. They are of the kind of the so‐called semilocal defects, and show richer properties than those previously known in another type of Higgs models.

Generating functions for characters and weight multiplicities of irreducible (4)-modules

Generating functions for the characters of the irreducible representations of simple Lie algebras are rational functions where both the numerator and denominator can be expressed as polynomials in the characters corresponding to the fundamental weights. They encode much information on the representation theory of the algebra, but their explicit expressions are in general very complicated. In fact, it seems that rank three is the highest rank tractable. In this paper, we use a method based on the quantum Calogero-Sutherland model to compute the full generating function for the characters of irreducible modules over the complex Lie algebra (4), and exploit this result to obtain also generating functions giving the multiplicities of some low order weights in all representations. We have applied the same method to compute the generating function for the characters of the modules the other rank three simple Lie algebras, but in these cases the full expressions are very long and appear only in the arXiv version of the paper (arXiv:1705.03711 [math-ph]). Nevertheless, when the generating functions are limited to some particular subsets of characters, the results are quite simple and we present them here.