A perturbative approach to the quantum elliptic Calogero-Sutherland model

We solve perturbatively the quantum elliptic Calogero-Sutherland model in the regime in which the quotient between the real and imaginary semiperiods of the Weierstrass ${\cal P}$ function is smallComment: 6 pages, no figure

Dissecting zero modes and bound states on BPS vortices in Ginzburg-Landau superconductors

In this paper the zero modes of fluctuation of cylindrically symmetric self-dual vortices are analyzed and described in full detail. These BPS topological defects arise at the critical point between Type II and Type I superconductors, or, equivalently, when the masses of the Higgs particle and the vector boson in the Abelian Higgs model are equal. In addition, novel bound states of Higss and vector bosons trapped by the self-dual vortices at their core are found and investigated.Comment: 29 pages, 51 figure

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 shown

Two Species of Vortices in a massive Gauged Non-linear Sigma Model

Non-linear sigma models with scalar fields taking values on $\mathbb{C}\mathbb{P}^n$ complex manifolds are addressed. In the simplest $n=1$ case, where the target manifold is the $\mathbb{S}^2$ sphere, we describe the scalar fields by means of stereographic maps. In this case when the $\mathbb{U}(1)$ symmetry is gauged and Maxwell and mass terms are allowed, the model accommodates stable self-dual vortices of two kinds with different energies per unit length and where the Higgs field winds at the cores around the two opposite poles of the sphere. Allowing for dielectric functions in the magnetic field, similar and richer self-dual vortices of different species in the south and north charts can be found by slightly modifying the potential. Two different situations are envisaged: either the vacuum orbit lies on a parallel in the sphere, or one pole and the same parallel form the vacuum orbit. Besides the self-dual vortices of two species, there exist BPS domain walls in the second case. Replacing the Maxwell contribution of the gauge field to the action by the second Chern-Simons secondary class, only possible in $(2+1)$-dimensional Minkowski space-time, new BPS topological defects of two species appear. Namely, both BPS vortices and domain ribbons in the south and the north charts exist because the vacuum orbit consits of the two poles and one parallel. Formulation of the gauged $\mathbb{C}\mathbb{P}^2$ model in a Reference chart shows a self-dual structure such that BPS semi-local vortices exist. The transition functions to the second or third charts break the $\mathbb{U}(1)\times\mathbb{S}\mathbb{U}(2)$ semi-local symmetry, but there is still room for standard self-dual vortices of the second species. The same structures encompassing $N$ complex scalar fields are easily generalized to gauged $\mathbb{C}\mathbb{P}^N$ models.Comment: 39 pages, 23 figures (extended version), to be published in JHE

On the solitons of the Chern-Simons-Higgs model

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 . 1 Introduction. For several years, the self-dual structure of the Chern-Simons-Higgs model [1, 2] has attracted the attention of theorists, giving rise to a large body of work on the subject both from the physical and mathematical points of view (see [3] for a review and a comprehensive list of references). The CSH model belongs to a family of generalized Abelian Higgs models [4] and one of the most ..