Medley in finite temperature field theory

I discuss three subjects in thermal field theory: why in \sun gauge theories the \zn symmetry is broken at high (instead of low) temperature, the possible singularity structure of gauge variant propagators, and the problem of how to compute the viscosity from the Kubo formula.Comment: LaTeX file, 11 pages, BNL-P-2/92 (December, 1992

Gauge invariance of the color-superconducting gap on the mass shell

The gap parameter for color superconductivity is expected to be a gauge invariant quantity, at least on the appropriate mass shell. Computing the gap to subleading order in the QCD coupling constant, g, we show that the prefactor of the exponential in 1/g is gauge dependent off the mass shell, and independent of gauge on the mass shell.Comment: 8 pages, Proceedings of the Conference on Statistical QCD, Bielefeld, August 26 - 30, 200

Color superconductivity in cold, dense quark matter

We review what is different and what is similar in a color superconductor as compared to an ordinary BCS superconductor. The parametric dependence of the zero-temperature gap on the coupling constant differs in QCD from that in BCS theory. On the other hand, the transition temperature to the superconducting phase is related to the zero-temperature gap in the same way in QCD as in BCS theory.Comment: 11 pages, 1 figure, proceedings of the "Fifth Workshop on QCD", Villefranche, Jan. 3-7, 200

N=1 Supersymmetric Spin-Charge Separation in effective gauge theories of planar magnetic superconductors

We present a N=1 Supersymmetric extension of a spin-charge separated effective $SU(2)\times U_S(1)$ `particle-hole' gauge theory of excitations about the nodes of the gap of a d-wave planar magnetic superconductor. The supersymmetry is achieved without introducing extra degrees of freedom, as compared to the non-supersymmetric models. The only exception, the introduction of gaugino fieds, finds a natural physical interpretation as describing interlayer coupling in the statistical model. The low-energy continuum theory is described by a relativistic (2+1)-dimensional supersymmetric $CP^1$ $\sigma$-model with Gross-Neveu-Thirring-type four-fermion interactions. We emphasize the crucial r\^ole of the $CP^1$ constraint in inducing a non-trivial dynamical mass generation for fermions (and thus superconductivity), in a way compatible with manifest N=1 supersymmetry. We also give a preliminary discussion of non-perturbative effects. We argue that supersymmetry suppresses the dangerous for superconductivity instanton contributions to the mass of the perturbatively massless gauge boson of the unbroken U(1) subgroup of SU(2). Finally, we point out the possibility of applying these ideas to effective gauge models of spin-charge separation in one-space dimensional superconducting chains of holons, which, for example, have recently been claimed to be important in the stripe phase of underdoped cuprates.Comment: 19 pages LATEX (minor misprints in formula (43) corrected

Numerical simulation of random paths with a curvature dependent action

We study an ensemble of closed random paths, embedded in R^3, with a curvature dependent action. Previous analytical results indicate that there is no crumpling transition for any finite value of the curvature coupling. Nevertheless, in a high statistics numerical simulation, we observe two different regimes for the specific heat separated by a rather smooth structure. The analysis of this fact warns us about the difficulties in the interpretation of numerical results obtained in cases where theoretical results are absent and a high statistics simulation is unreachable. This may be the case of random surfaces.Comment: 9 pages, LaTeX, 4 eps figures. Final version to appear in Mod. Phys. Lett.

Application of a multi-site mean-field theory to the disordered Bose-Hubbard model

We present a multi-site formulation of mean-field theory applied to the disordered Bose-Hubbard model. In this approach the lattice is partitioned into clusters, each isolated cluster being treated exactly, with inter-cluster hopping being treated approximately. The theory allows for the possibility of a different superfluid order parameter at every site in the lattice, such as what has been used in previously published site-decoupled mean-field theories, but a multi-site formulation also allows for the inclusion of spatial correlations allowing us, e.g., to calculate the correlation length (over the length scale of each cluster). We present our numerical results for a two-dimensional system. This theory is shown to produce a phase diagram in which the stability of the Mott insulator phase is larger than that predicted by site-decoupled single-site mean-field theory. Two different methods are given for the identification of the Bose glass-to-superfluid transition, one an approximation based on the behaviour of the condensate fraction, and one of which relies on obtaining the spatial variation of the order parameter correlation. The relation of our results to a recent proposal that both transitions are non self-averaging is discussed.Comment: Accepted for publication in Physical Review