Towards holographic color superconductivity in QCD

We extend the holographic V-QCD model by introducing a charged scalar field sector to represent the condensation of paired quark matter in the deconfined phase. By incorporating this new sector into the previously established framework for nuclear and quark matter, we obtain a phase diagram that, in addition to the first-order deconfinement transition and its critical end-point, also features a second-order transition between paired and unpaired quark matter. The critical temperature for quark pairing exhibits only a mild dependence on the chemical potential and can reach values as high as T_\mathrm{crit} ≈ 30 MeV <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> <mml:mi mathvariant="normal">r</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> <mml:mi mathvariant="normal">t</mml:mi> </mml:mrow> </mml:msub> <mml:mo>≈</mml:mo> <mml:mn>30</mml:mn> <mml:mi>M</mml:mi> <mml:mi>e</mml:mi> <mml:mi>V</mml:mi> </mml:mrow> </mml:math> . Comparison of the growth rate for the formation of homogeneous paired phases to the growth rate of previously discovered modulated phases suggests that the former is subdominant to the latter.