Thermal fluctuations of gauge fields and first order phase transitions in color superconductivity

We study the effects of thermal fluctuations of gluons and the diquark pairing field on the superconducting-to-normal state phase transition in a three-flavor color superconductor, using the Ginzburg-Landau free energy. At high baryon densities, where the system is a type I superconductor, gluonic fluctuations, which dominate over diquark fluctuations, induce a cubic term in the Ginzburg-Landau free energy, as well as large corrections to quadratic and quartic terms of the order parameter. The cubic term leads to a relatively strong first order transition, in contrast with the very weak first order transitions in metallic type I superconductors. The strength of the first order transition decreases with increasing baryon density. In addition gluonic fluctuations lower the critical temperature of the first order transition. We derive explicit formulas for the critical temperature and the discontinuity of the order parameter at the critical point. The validity of the first order transition obtained in the one-loop approximation is also examined by estimating the size of the critical region.