| Summary: | Abstract We investigate the order of the color superconducting phase transition using the functional renormalization group approach. We analyze the Ginzburg-Landau effective theory of color superconductivity and more generic scalar SU(N c) gauge theories by calculating the β function of the gauge coupling in arbitrary dimension d based on two different regularization schemes. We find that in d = 3, due to gluon fluctuation effects, the β function never admits an infrared fixed point solution. This indicates that, unlike the ordinary superconducting transition, color superconductivity can only show a first-order phase transition.
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