Spatially Modulated Phase in Holographic Quark-Gluon Plasma

TL;DR

This work demonstrates a holographic realization of a spatially modulated phase in a quark-gluon plasma by examining the Sakai-Sugimoto model with D8/\overline{D8} branes carrying a U(1) gauge field governed by a DBI action plus a Chern-Simons term. The authors show that the worldvolume Chern-Simons coupling $\alpha$ drives a tachyonic instability at finite baryon density when $\alpha>\alpha_{\rm crit}=1/4$, and in the deconfined phase with $\alpha=3/4$ a smooth finite-density background exists. Through linear analysis, they extract a critical density $\rho_{\rm crit}$ above which a nonzero-momentum mode destabilizes the homogeneous solution, and they compute the nonlinear end-point, revealing a spatially modulated phase with a characteristic momentum $|k|/R \sim 10 T$ and accompanying vector/axial baryon currents. The results map to QCD-like parameters, suggesting a new density-wave phase in holographic quark-gluon plasma and providing a concrete, gravity-based mechanism for spatially modulated order at finite density.

Abstract

We present a string theory construction of a gravity dual of a spatially modulated phase. In our earlier work, we showed that the Chern-Simons term in the 5-dimensional Maxwell theory destabilizes the Reissner-Nordstrom black holes in anti-de Sitter space if the Chern-Simons coupling is sufficiently high. In this paper, we show that a similar instability is realized on the worldvolume of 8-branes in the Sakai-Sugimoto model in the quark-gluon plasma phase. We also construct and analyze a non-linear solution describing the end-point of the transition. Our result suggests a new spatially modulated phase in quark-gluon plasma when the baryon density is above 0.8 N_f fm^{-3} at temperature 150 MeV.

Figures (3)

• Figure 1: The critical quark density $\tilde{\rho}$ as a function of the Chern-Simons coupling $\alpha$.
• Figure 2: Static normalizable solutions exist along this curve in the $h_0$-$k$ plane, when $\alpha=\frac{3}{4}$ and $\tilde{\rho}=5 u_T^{5/2}$. The minimum free energy occurs at $k= 2.35 u_T^{1/2}$, which is slightly larger than $k$ for the maximum value of $h_0$.
• Figure 3: The expectation value of the dual current operator $\tilde{\left<J\right>}$ as a function of $\tilde{\rho}$ at $\alpha=\frac{3}{4}$.