Non-Fermi Liquid Behaviour, the BRST Identity in the Dense Quark-Gluon Plasma and Color Superconductivity

At sufficiently high baryon densities, the physics of a dense quark-gluon plasma may be investigated through the tools of perturbative QCD. This approach has recently been successfully applied to the study of color superconductivity, where the dominant di-quark pairing interaction arises from one gluon exchange. Screening in the plasma leads to novel behaviour, including a remarkable non-BCS scaling of T_C, the transition temperature to the color superconducting phase. Radiative corrections to one gluon exchange were previously considered and found to affect T_C. In particular, the quark self-energy in a plasma leads to non-Fermi liquid behaviour and suppresses T_C. However, 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 radiative corrections at first appears rather surprising, as the BRST identity connects the self-energy to the vertex corrections. Nevertheless, as we demonstrate, there is in fact no contradiction with the BRST identity, at least to leading log 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.