R. Musto

Supersymmetric Strings and Color Confinement

The (infinite-dimensional) supersymmetry algebra in 1 + 1 space-time dimension is extended in order to incorporate, in a non-trivial way, an internal symmetry. It turns out that this requirement implies that the internal symmetry is realized as a local gauge symmetry. Moreover, it is possible to construct string-like models with this underlying symmetry, where colour confinement is exactly realized as a consequence of the gauge constraints.

Dual String with U(1) Color Symmetry

Abstract The string model with a U(1) colour symmetry is analyzed in detail. It is shown that the critical dimension of this model is D = 2. There are no tachyons in the U(1) string. Moreover the massless ground state is the only physical particle of the spectrum. All other states are decoupled because of the gauge conditions. The n -point amplitudes of the U(1) string are derived and shown to be equivalent to the tree diagrams of a conventional non-polynomial field theory in two dimensions, namely the non-linear σ model where the pion particle is identified with the massless ground state of the string with an isotopic Chan-Paton symmetry.

Dual String Models with Nonabelian Color and Flavor Symmetries

Abstract Dual string models with non-Abelian colour and flavour symmetries are investigated. For the exceptional case of SU(2) as a gauge colour symmetry a conventional string formulation is given and it is shown that the particles of the spectrum, which are colour singlets, are classified according to representations of a flavour group SU(2). The model turns out to contain ghosts independently of the value of the space-time dimension. This is also the case for models based on an O( N ) underlying colour symmetry.

Lattice CPN−1 models and their large-N behaviour

Abstract Two different lattice actions reproducing the CPN−1 model in the continuum are discussed and, in the two cases, strong and weak coupling expansions relative to different physical quantities are obtained. Large-N behaviour is analyzed by evaluating the limiting value of the two partition functions. In neither case does a smooth transition seem possible between strong and weak coupling regions for the limiting model.

The transition from the lattice to the continuum: CPN−1 models at large N

Abstract We study in detail the large N solution for the CP N −1 models on a euclidean lattice and their phase structure in D dimensions. In the two-dimensional case, we evaluate some physical quantities and discuss their behaviour in the continuum limit. In particular, for the internal energy, we found the analytic expression for the perturbative tail which, at large β, obscures the predicted renormalization group behaviour; such a tail, which, as we show, is reproduced by a mean field calculation at N =∞, must be subtracted in order to define a suitable scaling quantity. We also investigated the behaviour of the topological charge and we found no perturbative tail in agreement with previous Luschers results. Finally, some aspects of the supersymmetric case are discussed.

The anomaly term in the N=2 supersymmetric gauge theory

Abstract The Schwinger slowly varying field approximation is used to compute the terms in the effective lagrangian that reproduce the anomalies of the underlying theory. This method has been applied to extract the anomaly term in the case of pure N = 2 supersymmetric Yang-Mills theory.

Coulomb gas approach to quantum Hall effect

Abstract We show that single and multiparticle wave functions for both electrons and anyons relevant to the QHE can be obtained in a consistent way using Coulomb gas conformal Vertex operators. The values of the allowed charges are determined by the periodicity properties of the collective correlation functions on the torus.

Covariant multitadpole operator and bosonization in fermionic strings

Abstract Using the bosonization technique we construct the tadpole operator for a scalar field with anomaly Q on a general Riemann surface. Specifying to the case Q = 2 we derive the multitadpole operator for the fermionic string and show that it has the expected singularity cancellations.

Mass gap and universality for euclidean O(N) and CPN−1 models

Abstract From a suitably defined correlation function we evaluate the strong coupling expansion for the mass gap of an euclidean version of the O( N ) models in 2D. Good agreement is found for N = 0, 1 and 2 with the known values of the critical temperature and for N ⩾ 3 with the continuum mass gap as evaluated in an hamiltonian approach. Another test of universality based on the use of an asymmetric lattice also yields good results. An analogous discussion for the CP N −1 models is performed.

1/N contribution to physical quantities in the lattice O(N) σ-model

Abstract We evaluate the 1/N contribution to the mass gap and to the magnetic susceptibility for the two-dimensional O(N) nonlinear σ-model with standard lattice action. The same quantities are also obtained through a strong coupling analysis and found to be in good agreement with the direct evaluation. The relations with the results for different choices of the action are discussed.