Nathan Weiss

Gauge Theories With Imaginary Chemical Potential and the Phases of {QCD}

The phase structure of gauge theories with fermions as a function of imaginary chemical potential is related to the confining properties of the theory. It is controlled by a remnant of the ZN which is present in the absence of fermions. At high temperature the theory has a first-order phase transition as a function of imaginary chemical potential . This transition is expected to be absent in the low-temperature phase. Monte Carlo simulations are proposed which would check these ideas. It is shown that properties of the theory at nonzero fermion density can be deduced from its behavior at finite imaginary chemical potential.

Quantum fluctuations of Wilson loops from string models

Abstract We discuss the impact of quadratic quantum fluctuations on the Wilson loop extracted from classical string theory. We show that a large class of models, which includes the near horizon limit of D p branes with 16 supersymmetries, admits a Luscher type correction to the classical potential. For a BPS configuration of a single quark in the AdS 5 × S 5 model, we show that the bosonic and the fermionic determinants cancel, in particular confirming the absence of divergences. We find that for the Wilson loop in that model, however, there is no such cancellation. For string models that correspond to gauge theories in the confining phase, we show that the correction to the potential is of a Luscher type and is attractive.

Possible origins of a small, nonzero cosmological constant

Abstract The idea that the cosmological constant Λ may have a small, nonzero value (Λ ∼ (10 −33 eV) 2 ) has been recently revived in attempts to understand several cosmological issues. Despite the fact that such a small, nonzero Λ is aesthetically unappealing the issue of its existence will eventually be decided by experiments. In this paper the implications to particle physics of the existence of such a small, nonzero value of Λ are examined. Models are described in which the ground state of the system is assumed to have a cosmological constant equal to zero but in which we are not, presently in this ground state. The possibility that this deviation from the ground state leads to such a small, effective cosmological constant is studied.

Area law and continuum limit in “induced QCD”☆

We investigate a class of operators with non-vanishing averages in a D-dimensional matrix model recently proposed by Kazakov and Migdal. Among the operators considered are “filled Wilson loops” which are the most reasonable counterparts of Wilson loops in the convensional Wilson formulation of lattice QCD. The averages of interest are presented as partition functions of certain 2-dimensional statistical systems with nearest neighbor interactions. The “string tension” α′, which is the exponent in the area law for the “filled Wilson loop” is equal to the free energy density of the corresponding statistical system. The continuum limit of the Kazakov-Migdal model corresponds to the critical point of this statistical system. We argue that in the large N limit this critical point occurs at zero temperature. In this case we express α′ in terms of the density of eigenvalues of the matrix-valued master field. We show that the properties of the continuum limit and the description of how this limit is approached is very unusual and differs drastically from what occurs in both the Wilson theory (S ∝ (Tr Π U + c.c)) and in the “adjoint” theory (S ∝ |Tr Π U|2). Instead, the continuum limit of the model appears to be intriguingly similar to a c > 1 string theory.

Induced QCD and hidden local ZN symmetry.

We show that a lattice model for induced lattice QCD which was recently proposed by Kazakov and Migdal has a Z[sub [ital N]] gauge symmetry which, in the strong coupling phase, results in a local confinement where only color singlets are allowed to propagate along links and all Wilson loops for nonsinglets average to zero. We argue that if this model is to give QCD in its continuum limit, it must have a phase transition. We give arguments to support the presence of such a phase transition.

3D field theory model of a parity invariant anyonic superconductor

Abstract We present a (2+1)-dimensional field theory model of a parity invariant system of anyons and show that when there is a finite density of particles the model superconducts electric current and exhibits a Meissner effect. We also discuss a parity invariant non-anyonic model which is superconducting even at zero density.

ZN domains in gauge theories with fermions at high temperatures

Abstract At high temperatures, some SU (N) gauge theories with fermions have metastable states related to the ZN symmetry of the theory. It has recently been argued that the possible existence of domains of these metastable states may lead to some interesting cosmological consequences. We show that these states, generically, have unaacceptable thermodynamic behavior. Their free energy F∝T4 with a positive proportionality constant. This leads not only to negative pressure but also to negative specific heat and, more seriously, to negative entropy. We argue that although such domains are important in the euclidean theory, they cannot be interpreted as physical domains in Minkowski space. This conclusion remains valid even if sufficient color singlet particles (such as leptons and weak gauge bosons) are added to the system to make the total free energy negative.

CONTINUUM LIMITS OF “INDUCED QCD”: LESSONS OF THE GAUSSIAN MODEL AT d=1 AND BEYOND

We analyze the scalar field sector of the Kazakov-Migdal model of induced QCD. We present a detailed description of the simplest one-dimensional (d=1) model which supports the hypothesis of wide applicability of the mean-field approximation for the scalar fields and the existence of critical behavior in the model when the scalar action is Gaussian. Despite the occurrence of various nontrivial types of critical behavior in the d=1 model as N→∞, only the conventional large N limit is relevant for its continuum limit. We also give a mean-field analysis of the N=2 model in anyd and show that a saddle point always exists in the region . In d=1 it exhibits critical behavior as . However when d>1 there is no critical behavior unless non-Gaussian terms are added to the scalar field action. We argue that similar behavior should occur for any finite N thus providing a simple explanation of a recent result of D. Gross. We show that critical behavior at d>1 and can be obtained by adding a logarithmic term to the scalar potential. This is equivalent to a local modification of the integration measure in the original Kazakov—Migdal model. Experience from previous studies of the Generalized Kontsevich Model implies that, unlike the inclusion of higher powers in the potential, this minor modification should not substantially alter the behavior of the Gaussian model.

Kazakov–Migdal model with logarithmic potential and the double Penner matrix model

The Kazakov–Migdal (KM) model is a U(N) lattice gauge theory with a scalar field in the adjoint representation but with no kinetic term for the gauge field. This model is formally soluble in the limit N→∞ though explicit solutions are available for a very limited number of scalar potentials. A ‘‘double Penner’’ model in which the potential has two logarithmic singularities provides an example of an explicitly soluble model. The formal solution to this double Penner KM Model is reviewed first. Special attention is paid to the relationship of this model to an ordinary (one) matrix model whose potential has two logarithmic singularities (the double Penner model). A detailed analysis is presented of the large N behavior of this double Penner model. The various one cut and two cut solutions are described and cases in which ‘‘eigenvalue condensation’’ occurs at the singular points of the potential are discussed. Then the consequences of our study for the KM model described above are discussed. The phase diagram...

EVALUATION OF OBSERVABLES IN THE GAUSSIAN N=∞ KAZAKOV-MIGDAL MODEL

We examine the properties of observables in the Kazakov-Migdal model. We present explicit formulae for the leading asymptotics of adjoint Wilson loops as well as some other observables for the model with a Gaussian potential. We discuss the phase transiton in the large