Dirac operator as a random matrix and the quenched limit of QCD with chemical potential

The behavior of quenched QCD at nonzero chemical potential $\mu$ has been a long-standing puzzle. An explicit solution is found using the random matrix approach to chiral symmetry breaking. At nonzero $\mu$ the quenched QCD is not a simple $n\to0$ limit of a theory with $n$ quarks: a naive `replica trick' fails. A limit that leads to the quenched QCD is that of a theory with $2n$ quarks: $n$ quarks with original action and $n$ quarks with conjugate action.Comment: 3 pages, espcrc, 2 figures. Talk presented at LATTICE96(finite temperature

Absence of Physical Walls in Hot Gauge Theories

This paper shows that there are no {\em physical} walls in the deconfined, high-temperature phase of $Z(2)$ lattice gauge theory. In a Hamiltonian formulation, the interface in the Wilson lines is not physical. The line interface and its energy are interpreted in terms of physical variables. They are associated with a difference between two partition functions. One includes only the configurations with even flux across the interface. The other is restricted to odd flux. Also, with matter present, there is no physical metastable state. However, the free energy is lowered by the matter. This effect is described in terms of physical variables.Comment: 25 pages, Revte

The Degrees of Freedom in Hot Quenched QCD

In quenched QCD, on lattices with \nt=4, the absence of a pole in the pseudoscalar meson channel for $T>T_c$ is demonstrated. A set of effective 4-fermi couplings is extracted. It is observed that this coupling is small in the vector channel for all $T>T_c$, but not in the pseudoscalar channel. The temperature dependence of hadronic parameters below \tc{} is found to be small. NOTE: Latex source, no figures, needs espcrc2.sty from hep-lat macros.Comment: 3 pages, HLRZ 92-7

Relation between color-deconfinement and chiral restoration

We discuss the relation between the Polyakov loop and the chiral order parameter at finite temperature by using an effective model. We clarify why and how the pseudo-critical temperature associated with the Polyakov loop should coincide with that of the chiral condensate.Comment: Contributed to the XXI International Symposium on Lattice Field Theory (Lattice2003(nonzero)), Tsukuba, July 15-19, 200

SU(4) pure-gauge string tensions

In response to recently renewed interests in SU(N) pure-gauge dynamics with large N, both from M/string duality and from finite-temperature QCD phase structure, we calculate string tensions acting between the fundamental 4, diquark 6 and other color charges in SU(4) pure-gauge theory at temperatures below the deconfining phase change and above the bulk phase transition. Our results suggest 4 and 6 representations have different string tensions, with a ratio of about 1.3. We also found the deconfining phase change is not strong.Comment: LATTICE98(hightemp

Spontaneous Breaking of Flavor Symmetry and Parity in the Nambu-Jona-Lasinio Model with Wilson Fermions

We study the lattice \njl~model with two flavors of Wilson fermions in the large $N$ limit, where $N$ is the number of `colors'. For large values of the four-fermion coupling we find a phase in which both, flavor symmetry and parity, are spontaneously broken. In accordance with general expectations there are three massless pions on the phase boundary, but only two of them remain massless inside the broken phase. This is analogous to earlier results obtained in lattice QCD, indicating that this behavior is a very general feature of the Wilson term.Comment: 7 pages, 4 figures, LATEX, tared and uuencode