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We study the effects of thermal fluctuations of gluons and the diquarkpairing field on the superconducting-to-normal state phase transition in athree-flavor color superconductor, using the Ginzburg-Landau free energy. Athigh baryon densities, where the system is a type I superconductor, gluonicfluctuations, which dominate over diquark fluctuations, induce a cubic term inthe Ginzburg-Landau free energy, as well as large corrections to quadratic andquartic terms of the order parameter. The cubic term leads to a relativelystrong first order transition, in contrast with the very weak first ordertransitions in metallic type I superconductors. The strength of the first ordertransition decreases with increasing baryon density. In addition gluonicfluctuations lower the critical temperature of the first order transition. Wederive explicit formulas for the critical temperature and the discontinuity ofthe order parameter at the critical point. The validity of the first ordertransition obtained in the one-loop approximation is also examined byestimating the size of the critical region.Comment: 12 pages, 4 figures, final version published in Phys. Rev.

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