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

Can we study Quark Matter in the Quenched Approximation?

We study a quenched SU(2) lattice gauge theory in which, in an attempt to distinguish between timelike and spacelike gauge fields, the gauge ensemble {U_mu} is generated from a 3 dimensional gauge-Higgs model, the timelike link variables being "reconstructed" from the Higgs fields. The resulting ensemble is used to study quenched quark propagation with non-zero chemical potential mu; in particular, the quark density, chiral and superfluid condensates, meson, baryon and gauge-fixed quark propagators are all studied as functions of mu. While it proves possible to alter the strength of the inter-quark interaction by changing the parameters of the dimensionally reduced model, there is no evidence for any region of parameter space where quarks exhibit deconfined behaviour or thermodynamic observables scale as if there were a Fermi surface.Comment: 31 pages, 20 figures, enhanced discussion and analysis of finite volume effects, version accepted for publication by Nucl. Phys.