Holographic Method On The Critical Behavior Of QCD Chiral Phase Transitions

Quantum chromodynamics(QCD)is the basic theory describing strong interactions.Because of the asymptotic freedom of QCD vacuum,perturbed QCD can well deal with QCD problem in the high energy region and is consistent with a large number of high energy experimental results.However,it has been found that perturbed QCD cannot deal with the strong coupling problem of QCD in the low-energy region,so the holographic method developed by AdS/CFT duality conjecture becomes one of the powerful methods to deal with the strong coupling problem of QCD.The main content of this paper is extracting the critical exponent of the chiral phase transition in the soft wall model of the holographic framework,and conducting a comprehensive analysis of the universal class in the phase structure,so as to pave the way for a more comprehensive reaction system in the future.In this paper,we first introduce the background knowledge of QCD vacuum,such as asymptotic freedom,color confinement and spontaneous breaking of chiral symmetry.In order to prepare for the study of chiral phase transition critical exponent,we introduce the theory of phase transition,introduce the scaling relation of critical exponent and take NJL model as an example to describe the chiral phase transition mechanism.Then,we introduce the origin,principle and duality of holographic method,and describe the spontaneous breaking mechanism of chiral symmetry and the process of chiral phase transition in the soft wall model,which is a holographic model.On this basis,we extract the critical exponents of different flavor numbers and quark mass conditions respectively through numerical calculation and analytical derivation.Based on the phase diagram,we believe that there is a ”tri-critical” point on the second-order phase transition line of the phase diagram,and the ”tri-critical” point is divided into three different universal classes.In addition,by redefining the Dilaton field,we find that the soft wall model has the possibility of exceed the mean field approximation,which lays a foundation for a more comprehensive reaction model in the future.