Noncommutative Wess-Zumino-Witten actions and their Seiberg-Witten invariance

We analyze the noncommutative two-dimensional Wess-Zumino-Witten model and its properties under Seiberg-Witten transformations in the operator formulation. We prove that the model is invariant under such transformations even for the noncritical (non chiral) case, in which the coefficients of the kinetic and Wess-Zumino terms are not related. The pure Wess-Zumino term represents a singular case in which this transformation fails to reach a commutative limit. We also discuss potential implications of this result for bosonization.Comment: Version to appear in Nuclear Physics

Integrable Systems for Particles with Internal Degrees of Freedom

We show that a class of models for particles with internal degrees of freedom are integrable. These systems are basically generalizations of the models of Calogero and Sutherland. The proofs of integrability are based on a recently developed exchange operator formalism. We calculate the wave-functions for the Calogero-like models and find the ground-state wave-function for a Calogero-like model in a position dependent magnetic field. This last model might have some relevance for matrix models of open strings.Comment: 10 pages, UVA-92-04, CU-TP-56

Description of identical particles via gauged matrix models : a generalization of the Calogero-Sutherland system

We elaborate the idea that the matrix models equipped with the gauge symmetry provide a natural framework to describe identical particles. After demonstrating the general prescription, we study an exactly solvable harmonic oscillator type gauged matrix model. The model gives a generalization of the Calogero-Sutherland system where the strength of the inverse square potential is not fixed but dynamical bounded by below.Comment: 1+10 pages, No figure, LaTeX; a reference added, title changed slightly, minor correction, to appear in Phys. Lett.

Quantum Hall states as matrix Chern-Simons theory

We propose a finite Chern-Simons matrix model on the plane as an effective description of fractional quantum Hall fluids of finite extent. The quantization of the inverse filling fraction and of the quasiparticle number is shown to arise quantum mechanically and to agree with Laughlin theory. We also point out the effective equivalence of this model, and therefore of the quantum Hall system, with the Calogero model.Comment: 18 pages; final version to appear in JHE

Recent developments in non-Abelian T-duality in string theory

We briefly review the essential points of our recent work in non-Abelian T-duality. In particular, we show how non-abelian T-duals can effectively describe infinitely high spin sectors of a parent theory and how to implement the transformation in the presence of non-vanishing Ramond fields in type-II supergravity.Comment: 8 pages, Proceedings contribution to the 10th Hellenic School on Elementary Particle Physics and Gravity, Corfu, Greece, September 201

Quasihole wavefunctions for the Calogero model

The one-quasihole wavefunctions and their norms are derived for the system of particles on the line with inverse-square interactions and harmonic confining potential.Comment: 9 pages, no figures, phyzzx.te

Quantum Hall states on the cylinder as unitary matrix Chern-Simons theory

We propose a unitary matrix Chern-Simons model representing fractional quantum Hall fluids of finite extent on the cylinder. A mapping between the states of the two systems is established. Standard properties of Laughlin theory, such as the quantization of the inverse filling fraction and of the quasiparticle number, are reproduced by the quantum mechanics of the matrix model. We also point out that this system is holographically described in terms of the one-dimensional Sutherland integrable particle system.Comment: 25 pages; final version to appear in JHE

Algebra of Observables for Identical Particles in One Dimension

The algebra of observables for identical particles on a line is formulated starting from postulated basic commutation relations. A realization of this algebra in the Calogero model was previously known. New realizations are presented here in terms of differentiation operators and in terms of SU(N)-invariant observables of the Hermitian matrix models. Some particular structure properties of the algebra are briefly discussed.Comment: 13 pages, Latex, uses epsf, 1 eps figure include