Non-Fermi liquid behavior, the Becchi-Rouet-Stora-Tyutin identity in the dense quark-gluon plasma, and color superconductivity - art. no. 054013

At sufficiently high baryon densities, the physics of a dense quark-gluon p lasma may be investigated through the tools of perturbative QCD. This appro ach has recently been successfully applied to the study of color supercondu ctivity, where the dominant di-quark pairing interaction arises from one gl uon exchange. Screening in the plasma leads to novel behavior, including a remarkable non-BCS scaling of T-C, the transition temperature to the color superconducting phase. Radiative corrections to one gluon exchange were pre viously considered and found to affect T-C. In particular, the quark self-e nergy in a plasma leads to non-Fermi liquid behavior and suppresses T-C. Ho wever, at the same time, the quark-gluon vertex was shown not to modify the result at leading order. This dichotomy between the effects of the radiati ve corrections a first appears rather surprising, as the BRST identity conn ects the self-energy to the vertex corrections. Nevertheless, as we demonst rate, there is in fact no contradiction with the BRST identity, at least to leading logarithmic order. This clarifies some of the previous statements on the importance of the higher order corrections to the determination of T -C and the zero temperature gap in color superconductivity.