The Hierarchy Principle and the Large Mass Limit of the Linear Sigma Model

In perturbation theory we study the matching in four dimensions between the linear sigma model in the large mass limit and the renormalized nonlinear sigma model in the recently proposed flat connection formalism. We consider both the chiral limit and the strong coupling limit of the linear sigma model. Our formalism extends to Green functions with an arbitrary number of pion legs,at one loop level,on the basis of the hierarchy as an efficient unifying principle that governs both limits. While the chiral limit is straightforward, the matching in the strong coupling limit requires careful use of the normalization conditions of the linear theory, in order to exploit the functional equation and the complete set of local solutions of its linearized form.Comment: Latex, 41 pages, corrected typos, final version accepted by IJT

Matrix Models, Argyres-Douglas singularities and double scaling limits

We construct an N=1 theory with gauge group U(nN) and degree n+1 tree level superpotential whose matrix model spectral curve develops an A_{n+1} Argyres-Douglas singularity. We evaluate the coupling constants of the low-energy U(1)^n theory and show that the large N expansion is singular at the Argyres-Douglas points. Nevertheless, it is possible to define appropriate double scaling limits which are conjectured to yield four dimensional non-critical string theories as proposed by Ferrari. In the Argyres-Douglas limit the n-cut spectral curve degenerates into a solution with n/2 cuts for even n and (n+1)/2 cuts for odd n.Comment: 31 pages, 1 figure; the expression of the superpotential has been corrected and the calculation of the coupling constants of the low-energy theory has been adde

The FLUKA Monte Carlo, non-perturbative QCD and Cosmic Ray cascades

The FLUKA Monte Carlo code, presently used in cosmic ray physics, contains packages to sample soft hadronic processes which are built according to the Dual Parton Model. This is a phenomenological model capable of reproducing many of the features of hadronic collisions in the non perturbative QCD regime. The basic principles of the model are summarized and, as an example, the associated Lambda-K production is discussed. This is a process which has some relevance for the calculation of atmospheric neutrino fluxes.Comment: Extended version of the work for the proceedings of the workshop on QCD at Cosmic Ray Energies, Erice, Aug. 30 - Sep. 4 2004, Ital

On the Hydrodynamic Equilibrium of a Rod in a Lattice Fluid

We model the behavior of a big (Brazil) nut in a medium of smaller nuts with a stochastic asymmetric simple exclusion dynamics of a polymer-monomer lattice system. The polymer or `rod' can move up or down in an external negative field, occupying N horizontal lattice sites where the monomers cannot enter. The monomers (at most one per site) or `fluid particles' are moving symmetrically in the horizontal plane and asymmetrically in the vertical direction, also with a negative field. For a fixed position of the rod, this lattice fluid is in equilibrium with a vertical height profile reversible for the monomers' motion. Upon `shaking' (speeding up the monomers) the motion of the `rod' dynamically decouples from that of the monomers resulting in a reversible random walk for the rod around an average height proportional to log N.Comment: 19 pages, 2 figure

Of Higgs, Unitarity and other Questions

On the verge of conclusive checks on the Standard Model by the LHC, we discuss some of the basic assumptions. The reason for this analysis stems from a recent proposal of an Electroweak Model based on a nonlinearly realized gauge group SU(2) X U(1), where, in the perturbative approximation, there is no Higgs boson. The model enjoys the Slavnov-Taylor identities and therefore the perturbative unitarity. On the other hand, it is commonly believed that the existence of the Higgs boson is entangled with the property of unitarity, when high energy processes are considered. The argument is based mostly on the Froissart bound and on the Equivalence Theorem. In this talk we briefly review some of our objections on the validity of such arguments. Some open questions are pointed out, in particular on the limit of zero mass for the vector mesons and on the fate of the longitudinal polarizations.Comment: 23 pages, 1 figure, presented by Ruggero Ferrari at the International Conference "Gauge Fields. Yesterday, Today, Tomorrow" in honor of A.A. Slavnov. Moscow, January 19-24 201

Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems

We study the spectrum of a random Schroedinger operator for an electron submitted to a magnetic field in a finite but macroscopic two dimensional system of linear dimensions equal to L. The y direction is periodic and in the x direction the electron is confined by two smooth increasing boundary potentials. The eigenvalues of the Hamiltonian are classified according to their associated quantum mechanical current in the y direction. Here we look at an interval of energies inside the first Landau band of the random operator for the infinite plane. In this energy interval, with large probability, there exist O(L) eigenvalues with positive or negative currents of O(1). Between each of these there exist O(L^2) eigenvalues with infinitesimal current O(exp(-cB(log L)^2)). We explain what is the relevance of this analysis to the integer quantum Hall effect.Comment: 29 pages, no figure

Bosonic Field Propagators on Algebraic Curves

In this paper we investigate massless scalar field theory on non-degenerate algebraic curves. The propagator is written in terms of the parameters appearing in the polynomial defining the curve. This provides an alternative to the language of theta functions. The main result is a derivation of the third kind differential normalized in such a way that its periods around the homology cycles are purely imaginary. All the physical correlation functions of the scalar fields can be expressed in terms of this object. This paper contains a detailed analysis of the techniques necessary to study field theories on algebraic curves. A simple expression of the scalar field propagator is found in a particular case in which the algebraic curves have $Z_n$ internal symmetry and one of the fields is located at a branch point.Comment: 26 pages, TeX + harvma