Extension to Imaginary Chemical Potential in a Holographic Model

TL;DR

This paper extends a holographic QCD model to include imaginary chemical potential, studying the phase diagram and RW transitions, and validates the model by comparing with lattice QCD results.

Contribution

It introduces an extension of a holographic model to the imaginary chemical potential region, analyzing phase transitions and the effects of back reaction, with a new bound on the color number.

Findings

Observed Roberge-Weiss transitions in the extended model.

Identified a lower bound on the color number for RW periodicity.

Validated the model against lattice QCD results near zero chemical potential.

Abstract

We extend a bottom up holographic model, which has been used in studying the color superconductivity in QCD, to the imaginary chemical potential ($\mu_I$) region, and the phase diagram is studied on the $\mu_I$-temperature (T) plane. The analysis is performed for the case of the probe approximation and for the background where the back reaction from the flavor fermions are taken into account. For both cases, we could find the expected Roberge-Weiss (RW) transitions. In the case of the back-reacted solution, a bound of the color number $N_c$ is found to produce the RW periodicity. It is given as $N_c\geq 1.2$. Furthermore, we could assure the validity of this extended model by comparing our result with the one of the lattice QCD near $\mu_I=0$.