Phase Transitions and Black Hole Stability in Gauged N = 8 Supergravity

TL;DR

This work analyzes planar, electrically dilatonic black holes in the $D=4$ gauged $\mathcal{N}=8$ supergravity STU/T^3 truncation and demonstrates that AdS solitons can complete the thermal phase space, signaling confinement in the dual field theory when the black hole becomes locally unstable. The authors derive the asymptotic holographic data, establish the equation of state $m = \frac{1}{A^{1/2}L}\prod_\Lambda (A^2L^2+Q_\Lambda^2)^{1/4}$, and perform a Hessian analysis to identify spinodal instability regions, then reformulate the problem in a grand canonical ensemble with a cubic constraint, yielding a parametric description of the stable region. They compute the Gibbs free energy for black holes and construct AdS soliton solutions with the same boundary data, showing a first-order phase transition between the two phases and a smooth continuation between branches at the stability boundary. The findings illuminate holographic confinement mechanisms in planar backgrounds and provide explicit, tractable criteria for stability and transitions in the $\mathcal{N}=8$ supergravity context, with implications for M-theory on $S^7$ and ABJM-like duals.

Abstract

It is well known that there is a region of parameter space where all purely electric, static, dilatonic black holes are unstable within the STU models of maximal supergravity. We show that, for planar black holes, it is possible to complete the thermal phase space with AdS solitons, in such a way that the instability of the black holes signals the onset of confinement in the dual field theory. The analysis is done for the $D=4$ STU model of maximal gauged supergravity which naturally uplift to M-theory on the $S^7$.

Figures (5)

• Figure 1: Stability region of the T${}^{3}$ model in the microcanonical ensemble.
• Figure 2: Boundary conditions for AdS solitons in the T${}^{3}$ model.
• Figure 3: Free energy density of the stable solutions of the T${}^{3}$ model in the grand canonical ensemble. Stable thermal states exist for $\omega_0\in [-1,-\frac{4}{27}]$.
• Figure 4: The boundary conditions that yield solitons for the T$^3$ model.
• Figure 5: Energy density of the branch of solitons with negative energy. We plot $\rho_0=\frac{\Delta^3}{(2\pi)^3}\rho_{sol}\in [-\frac{4}{27},0]$. The solutions at $\rho_0=0$ are supersymmetric.