The effect of charm quark on chiral phase transition in $N_f=2+1+1$ holographic QCD

Abstract: We investigate the effect of charm quark on the chiral phase transition of light quarks at finite temperature based on the four-flavor soft-wall holographic QCD model. In the massless limit, we find that the thermal chiral phase transition is of the second order in the four-quark flavor system. In the case with the massive charm quark and the massless light and strange quarks, the order of the phase transition changes to the first order. This is due to the quark flavor symmetry breaking which is associated with the violation of the $U(1)$ axial symmetry. Once the light and strange quarks get massive, the explicit chiral symmetry breaking becomes eminent, then the crossover phase transition is realized at the physical quark masses. We also map the order of the phase transition on a phase diagram in the quark mass plane where the light- and strange-quark masses are degenerate but differ from the value of the charm quark mass. This phase diagram is an extension of the conventional Columbia plot to the four-quark flavor system. The critical exponents related to the chiral phase transition are also addressed.