Analytic Study on Chiral Phase Transition in Holographic QCD

The chiral symmetry breaking ($\chi_{SB}$) is one of the most fundamental problems in QCD. In this paper, we calculate quark condensation analytically in a holographic QCD model dual to the Einstein-Maxwell-Dilaton (EMD) system coupled to a probe scalar field. We find that the black hole phase transition in the EMD system seriously affects $\chi_{SB}$. At small chemical potential, $\chi_{SB}$ behaves as a crossover. For large chemical potential $\mu>\mu_c$, $\chi_{SB}$ becomes first order with exactly the same transition temperature as the black hole phase transition by a bypass mechanism. The phase diagram we obtained is qualitatively consistent with the recent results from lattice QCD simulations and NJL models.
Comment: 23 pages, 8 figures. Fixed some typos. Added some discussion in "Introduction" and "Conclusion"