Abstract
We calculate the effective potential of the $2\mathrm{SC}/\mathrm{g}2\mathrm{SC}$ phases including vector condensates ($⟨g{A}_{z}^{6}⟩$ and $⟨g{A}_{z}^{8}⟩$) and study the gluonic phase and the single plane-wave Larkin-Ovchinnikov-Fulde-Ferrell state at nonzero temperature. Our analysis is performed within the framework of the gauged Nambu-Jona-Lasinio model. We compute potential curvatures with respect to the vector condensates and investigate the temperature dependence of the Meissner masses squared of gluons of color 4--7 and 8 in the neutral $2\mathrm{SC}/\mathrm{g}2\mathrm{SC}$ phases. The phase diagram is presented in the plane of temperature and coupling strength. The unstable regions for gluons 4--7 and 8 are mapped out on the phase diagram. We find that, apart from the case of strong coupling, the $2\mathrm{SC}/\mathrm{g}2\mathrm{SC}$ phases at low temperatures are unstable against the vector condensation until the temperature reaches tens of MeV.
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