Thermodynamics and Instabilities of a Strongly Coupled Anisotropic Plasma

TL;DR

This work constructs and analyzes a finite-temperature, strongly coupled anisotropic plasma via its IIB holographic dual, realized as a static, regular black brane with axion-dilaton backreaction from a uniform D7-brane density that sources a linearly varying theta-angle. The solution connects a UV AdS$_5$ region to an IR Lifshitz-like geometry, with anisotropy confined to the $z$-direction, and exhibits a conserved but anomalous holographic stress tensor whose trace encodes a conformal anomaly and introduces a renormalization scale $\mu$. The authors derive the thermodynamics, define the chemical potential conjugate to the D7-brane density, and map out a phase diagram in the $(a,T)$ plane featuring homogeneous and inhomogeneous (mixed) phases, including regimes of instability and phase separation reminiscent of weakly coupled plasmas and QCD at finite density. They also discuss the physical interpretation in terms of D7-brane backreaction, the role of the anomaly, and potential connections to cavitation and percolation phenomena, offering a controlled setting to explore anisotropic strongly coupled plasmas and Lifshitz-like IR physics. Overall, the work provides a detailed holographic framework for understanding how anisotropy and density affect thermodynamics, stability, and phase structure in a nonperturbative gauge theory, with potential implications for QGP phenomenology and condensed matter systems with Lifshitz scaling.

Abstract

We extend our analysis of a IIB supergravity solution dual to a spatially anisotropic finite-temperature N=4 super Yang-Mills plasma. The solution is static, possesses an anisotropic horizon, and is completely regular. The full geometry can be viewed as a renormalization group flow from an AdS geometry in the ultraviolet to a Lifshitz-like geometry in the infrared. The anisotropy can be equivalently understood as resulting from a position-dependent theta-term or from a non-zero number density of dissolved D7-branes. The holographic stress tensor is conserved and anisotropic. The presence of a conformal anomaly plays an important role in the thermodynamics. The phase diagram exhibits homogeneous and inhomogeneous (i.e. mixed) phases. In some regions the homogeneous phase displays instabilities reminiscent of those of weakly coupled plasmas. We comment on similarities with QCD at finite baryon density and with the phenomenon of cavitation.

Figures (13)

• Figure 1: D7-branes dissolved in the geometry.
• Figure 2: Log-log plot of the entropy density as a function of $a/T$, with $s^0$ defined as in eqn. (\ref{['entropyN=4']}). The dashed blue line is a straight line with slope $1/3$.
• Figure 3: Expansion coefficients ${\cal F}_4$ and ${\cal B}_4$. In (a) we fix $T= 1$ and plot ${\cal F}_4/T^4$ and ${\cal B}_4/T^4$ as functions of $a/T$. In (b) we fix $a= 1$ and plot ${\cal F}_4/a^4$ and ${\cal B}_4/a^4$ as functions of $T/a$. From the plots in (a) we can see that, as $a\to 0$, we recover the isotropic solution (\ref{['isotropic']}), since in this limit ${\cal B}_4\to 0$ and ${\cal F}_4\to -97.4 \simeq -\pi^4$.
• Figure 4: The energy and pressures normalized by their isotropic values (\ref{['EP0']}) as functions of $a/T$, with $T\simeq 0.33$ in (a) and $T\simeq 1.1$ in (b). We have chosen $c_\textrm{\tiny sch}=-1$ and $\mu=1$.
• Figure 5: The energy and pressures divided by $N_\textrm{\tiny c}^2 a^4$ as functions of $T/a$, with $a \simeq 0.34$ in (a) and $a\simeq 2.86$ in (b). We have chosen $c_\textrm{\tiny sch}=-1$ and $\mu=1$.