Holographic Vitrification

TL;DR

This work constructs a concrete holographic model—4D Einstein gravity with two U(1)s and a running scalar in AdS4—to realize stable and metastable black hole bound states at finite temperature and chemical potentials. In the probe limit, these bound states create a rugged free-energy landscape with an extensive configurational entropy, and their relaxation exhibits logarithmic aging governed by a broad distribution of barriers, mirroring key glassy dynamics. The authors map bulk bound-state configurations to localized charge and current densities in the dual CFT and discuss planar limits, hyperscaling-violating regimes, and transport implications, arguing that fragmented horizons realize holographic structural glasses. While the results are primarily in the probe regime, they establish a framework in which holography can capture both thermodynamic and dynamical aspects of glass formation, offering a controlled setting to explore dynamical heterogeneities and aging in strongly coupled quantum fluids. The work also outlines challenges for embedding such constructions in string theory and highlights directions for extending to fully backreacted, truly glassy holographic phases.

Abstract

We establish the existence of stable and metastable stationary black hole bound states at finite temperature and chemical potentials in global and planar four-dimensional asymptotically anti-de Sitter space. We determine a number of features of their holographic duals and argue they represent structural glasses. We map out their thermodynamic landscape in the probe approximation, and show their relaxation dynamics exhibits logarithmic aging, with aging rates determined by the distribution of barriers.

Figures (25)

• Figure 1.1: Electric (left) and magnetic (right) field lines for some bound charges. The bottom plane is the horizon, the top plane is the boundary. The vertical coordinate is the optical distance from the horizon (cf. (\ref{['opticaldist']})).
• Figure 4.1: AdS-Schwarzschild free energy $F$ for a black hole of size $u$ coupled to a heat bath at temperatures (from left to right) $\pi T = 0.75, 0.95, 1.15$. A local minimum corresponds to a perturbatively stable black hole, which is globally stable if it is negative. A local maximum corresponds to a perturbatively unstable black hole.
• Figure 4.2: Phase diagrams for the black hole background. On the left we have $\phi_1=0.4 \,\phi_0$ and on the right $\phi_1=\phi_0$. The different regions are labeled by a the signs of the free energies of the black hole solutions in the region. For example $(-\,+)$ is a region with two black holes, one with negative and one with positive free energy, while $(-)$ indicates a region with just one black hole, with negative free energy. Across the dotted lines either $\Delta_0$ or $\Delta_1$ changes sign. The white regions represent configurations where no black holes exist. The Hawking-Page transition occurs at the thick black line, terminating in the orange dot.
• Figure 4.3: Left: Planar black hole temperature $T/\phi_0$ as a function of $u_1/\phi_0$, for $\phi_1/\phi_0 = 0.1, 0.4, 0.495, 0.505, 0.7$, corresponding respectively to the dash-dotted, dashed and solid blue curves, and to the solid and dotted red curves. Lines of constant $T/\phi_0$ intersect the curves in two points or not at all, illustrating that for given intensive variables, there are always either two black hole solutions or none at all. Right: Planar black hole phase diagram. The colored region has two black holes, the white has none. It corresponds to the gaps in accessible temperatures for the curves on the left. The dotted lines denote the Reissner-Nordstrom locus, where one of the planar solutions has no scalar hair. In the white gap, the background becomes unstable to soaking up $Q_0$ charge as discussed in remark \ref{['upperwhitegap']} in the previous section.
• Figure 4.4: Lines of constant charge for ${}{P}^1=1$, $\pm {}{Q}_0 = 10^{-5},$$10^{-4}$, $10^{-3}$, $10^{-2}$, $10^{-1}$, $1/6$, $0.316$, $1$, with the larger values of $|{}{Q}_0|$ being closest to the $\phi_1=0$ axis at high temperatures. The value ${}{Q}_0 = 1/6$ corresponds to the Reissner-Nordstrom solution. In the lower half of the plane, the hue of the lines goes up according to entropy (going up in red to yellow direction), while in the upper half of the plane, the mass (=free energy) is indicated in this way. The lower values of $|{}{Q}_0|$ have the lower free energy and entropy. The stable and unstable branches connect at the boundary of the white gap.