Holographic anisotropic model for light quarks with confinement-deconfinement phase transition

Irina Ya Aref’Eva,Kristina Rannu,Pavel Slepov

doi:10.1007/jhep06(2021)090

Abstract

We present a five-dimensional anisotropic holographic model for light quarks supported by Einstein-dilaton-two-Maxwell action. This model generalizing isotropic holographic model with light quarks is characterized by a Van der Waals-like phase transition between small and large black holes. We compare the location of the phase transition for Wilson loops with the positions of the phase transition related to the background instability and describe the QCD phase diagram in the thermodynamic plane — temperature T and chemical potential μ. The Cornell potential behavior in this anisotropic model is also studied. The asymptotics of the Cornell potential at large distances strongly depend on the parameter of anisotropy and orientation. There is also a nontrivial dependence of the Cornell potential on the boundary conditions of the dilaton field and parameter of anisotropy. With the help of the boundary conditions for the dilaton field one fits the results of the lattice calculations for the string tension as a function of temperature in isotropic case and then generalize to the anisotropic one.

Highlights

Theory at short distances and Lattice QCD results at large distances
We present a five-dimensional anisotropic holographic model for light quarks supported by Einstein-dilaton-two-Maxwell action
We compare the location of the phase transition for Wilson loops with the positions of the phase transition related to the background instability and describe the QCD phase diagram in the thermodynamic plane — temperature T and chemical potential μ

Summary

Metric and EOM

Where L is the AdS-radius, b(z) is the warp factor, A(z) is its half-power, g(z) is the blackening function and ν is the parameter of anisotropy. Excluding anisotropy and normalizing to the AdS-radius, i.e. putting L = 1, ν = 1 and f2 = 0 into (2.5)–(2.10), one can get the expressions that fully coincide with the EOM. In this paper we assume a = 4.046, b = 0.01613, c = 0.227 to make our solution agree with results from [29] in the isotropic case. These values are due to the mass spectrum of ρ meson with its excitations and to the lattice results for the phase transition temperature. We use the same values of a, b and c for anisotropic case, as we still do not have anisotropic lattice data for the spectrum

Solution

Temperature and entropy

Temporal Wilson loops

Conclusion