Chiral phase transition: Effective field theory and holography

We consider the chiral phase transition relevant for QCD matter at finite temperature but with vanishing baryon density. Presumably, the chiral phase transition is of second order for two-flavor QCD in the chiral limit [F. Cuteri, On the order of the QCD chiral phase transition for different numbers of quark flavours, J. High Energy Phys. 11 (2021) 141.JHEPFG1029-847910.1007/JHEP11(2021)141]. Near the transition temperature, we apply the Schwinger-Keldysh formalism and construct a low-energy effective field theory for the system, in which fluctuations and dissipations are systematically captured. The dynamical variables involve the chiral charge densities and order parameter (chiral condensate). Via the holographic Schwinger-Keldysh technique, the effective action is further confirmed within a modified anti-de Sitter QCD model. With higher-order terms suitably neglected, the stochastic equations derived from the effective field theory resemble those of model F in the Hohenberg-Halperin classification. Within the effective field theory, we briefly discuss the spontaneous breaking of chiral symmetry and Goldstone modes.