Holographic calculation of the QCD crossover temperature in a magnetic field

Abstract

Lattice data for the QCD equation of state and the magnetic susceptibility computed near the crossover transition at zero magnetic field are used to determine the input parameters of a five dimensional Einstein-Maxwell-Dilaton holographic model. Once the model parameters are fixed at zero magnetic field, one can use this holographic construction to study the effects of a magnetic field on the equilibrium and transport properties of the quark-gluon plasma. In this paper we use this model to study the dependence of the crossover temperature with an external magnetic field. Our results for the pressure of the plasma and the crossover temperature are in quantitative agreement with current lattice data for values of the magnetic field $0\le eB\lesssim 0.3$ GeV${}^2$, which is the relevant range for ultrarelativistic heavy ion collision applications.

Comments: 31 pages, 6 figures, version accepted for publication in Physical Review D