Gauge Invariant Variational Approach with Fermions: the Schwinger Model

We extend the gauge invariant variational approach of Phys. Rev. D52 (1995) 3719, hep-th/9408081, to theories with fermions. As the simplest example we consider the massless Schwinger model in 1+1 dimensions. We show that in this solvable model the simple variational calculation gives exact results.Comment: 14 pages, 1 figur

Variational analysis of the deconfinement phase transition

We study the deconfining phase transition in 3+1 dimensional pure SU(N) Yang-Mills theory using a gauge invariant variational calculation. We generalize the variational ansatz of Phys. Rev. D52, 3719 (1995) to mixed states (density matrices) and minimize the free energy. For N > 3 we find a first order phase transition with the transition temperature of T_C = 450 Mev. Below the critical temperature the Polyakov loop has vanishing expectation value, while above T_C, its average value is nonzero. According to the standard lore this corresponds to the deconfining transition. Within the accuracy of our approximation the entropy of the system in the low temperature phase vanishes. The latent heat is not small but, rather, is of the order of the nonperturbative vacuum energy.Comment: 15 pages, correction of minor typos only, submitted to JHE

Angular Momentum Mixing in Crystalline Color Superconductivity

In crystalline color superconductivity, quark pairs form at non-zero total momentum. This crystalline order potentially enlarges the domain of color superconductivity in cold dense quark matter. We present a perturbative calculation of the parameters governing the crystalline phase and show that this is indeed the case. Nevertheless, the enhancement is modest, and to lowest order is independent of the strength of the color interaction.Comment: 9 pages, 2 figures, Revte

How the quark self-energy affects the color-superconducting gap

We consider color superconductivity with two flavors of massless quarks which form Cooper pairs with total spin zero. We solve the gap equation for the color-superconducting gap parameter to subleading order in the QCD coupling constant $g$ at zero temperature. At this order in $g$, there is also a previously neglected contribution from the real part of the quark self-energy to the gap equation. Including this contribution leads to a reduction of the color-superconducting gap parameter \f_0 by a factor b_0'=\exp \big[ -(\p ^2+4)/8 \big]\simeq 0.177. On the other hand, the BCS relation T_c\simeq 0.57\f_0 between \f_0 and the transition temperature $T_c$ is shown to remain valid after taking into account corrections from the quark self-energy. The resulting value for $T_c$ confirms a result obtained previously with a different method.Comment: Revtex, 8 pages, no figur

Gluon self-energy in a two-flavor color superconductor

The energy and momentum dependence of the gluon self-energy is investigated in a color superconductor with two flavors of massless quarks. The presence of a color-superconducting quark-quark condensate modifies the gluon self-energy for energies which are of the order of the gap parameter. For gluon energies much larger than the gap, the self-energy assumes the form given by the standard hard-dense loop approximation. It is shown that this modification of the gluon self-energy does not affect the magnitude of the gap to leading and subleading order in the weak-coupling limit.Comment: 21 pages, 6 figures, RevTeX, aps and epsfig style files require

Anomalous specific heat in high-density QED and QCD

Long-range quasi-static gauge-boson interactions lead to anomalous (non-Fermi-liquid) behavior of the specific heat in the low-temperature limit of an electron or quark gas with a leading $T\ln T^{-1}$ term. We obtain perturbative results beyond the leading log approximation and find that dynamical screening gives rise to a low-temperature series involving also anomalous fractional powers $T^{(3+2n)/3}$. We determine their coefficients in perturbation theory up to and including order $T^{7/3}$ and compare with exact numerical results obtained in the large-$N_f$ limit of QED and QCD.Comment: REVTEX4, 6 pages, 2 figures; v2: minor improvements, references added; v3: factor of 2 error in the T^(7/3) coefficient corrected and plots update

Quantum-critical pairing with varying exponents

We analyse the onset temperature T_p for the pairing in cuprate superconductors at small doping, when tendency towards antiferromagnetism is strong. We consider the model of Moon and Sachdev (MS), which assumes that electron and hole pockets survive in a paramagnetic phase. Within this model, the pairing between fermions is mediated by a gauge boson, whose propagator remains massless in a paramagnet. We relate the MS model to a generic \gamma-model of quantum-critical pairing with the pairing kernel \lambda (\Omega) \propto 1/\Omega^{\gamma}. We show that, over some range of parameters, the MS model is equivalent to the \gamma-model with \gamma =1/3 (\lambda (\Omega) \propto \Omega^{-1/3}). We find, however, that the parameter range where this analogy works is bounded on both ends. At larger deviations from a magnetic phase, the MS model becomes equivalent to the \gamma-model with varying \gamma >1/3, whose value depends on the distance to a magnetic transition and approaches \gamma =1 deep in a paramagnetic phase. Very near the transition, the MS model becomes equivalent to the \gamma-model with varying \gamma <1/3. Right at the magnetic QCP, the MS model is equivalent to the \gamma-model with \gamma =0+ (\lambda (\Omega) \propto \log \Omega), which is the model for color superconductivity. Using this analogy, we verified the formula for T_c derived for color superconductivity.Comment: 10 pages, 8 figures, submitted to JLTP for a focused issue on Quantum Phase Transition

Generalized Ward identity and gauge invariance of the color-superconducting gap

We derive a generalized Ward identity for color-superconducting quark matter via the functional integral approach. The identity implies the gauge independence of the color-superconducting gap parameter on the quasi-particle mass shell to subleading order in covariant gauge.Comment: 5 pages, 1 Postscript figure, uses Revte