Functional renormalization group approach to color superconducting phase transition

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<jats:title>A<jats:sc>bstract</jats:sc> </jats:title> <jats:p>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(<jats:italic>N</jats:italic> <jats:sub>c</jats:sub>) gauge theories by calculating the <jats:italic>β</jats:italic> function of the gauge coupling in arbitrary dimension <jats:italic>d</jats:italic> based on two different regularization schemes. We find that in <jats:italic>d</jats:italic> = 3, due to gluon fluctuation effects, the <jats:italic>β</jats:italic> 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.</jats:p>

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