An effective matrix model for dynamical end of the world branes in Jackiw-Teitelboim gravity

TL;DR

This work constructs a nonperturbative matrix-model dual for JT gravity with dynamical end-of-the-world branes, showing that brane loops deform the matrix potential via a brane-induced term δV and that the IR spectrum is governed by a string equation linking UV data to the low-energy edge E0. It reveals a phase structure including a one-cut JT-like regime and a nonperturbative Y-shaped phase on complex contours, where a fraction of eigenvalues become complex and are interpreted as metastable black-hole states. The authors connect these matrix-model insights to an effective W(Φ) dilaton gravity, find an induced-gravity scaling S0,eff ∼ log K for large brane flavor K, and analyze Hawking-Page-type transitions with Dirichlet-Neumann branes to restore stability and provide a canonical ensemble. Overall, the work demonstrates that UV brane physics profoundly shapes IR JT gravity through a regulated, nonperturbatively defined matrix model and offers a concrete route toward a more conventional UV completion of JT gravity behind horizons.

Abstract

We study Jackiw-Teitelboim gravity with dynamical end of the world branes in asymptotically nearly AdS$_2$ spacetimes. We quantize this theory in Lorentz signature, and compute the Euclidean path integral summing over topologies including dynamical branes. The latter will be seen to exactly match with a modification of the SSS matrix model. The resolution of UV divergences in the gravitational instantons involving the branes will lead us to understand the matrix model interpretation of the Wilsonian effective theory perspective on the gravitational theory. We complete this modified SSS matrix model nonperturbatively by extending the integration contour of eigenvalues into the complex plane. Furthermore, we give a new interpretation of other phases in such matrix models. We derive an effective $W(Φ)$ dilaton gravity, which exhibits similar physics semiclassically. In the limit of a large number of flavors of branes, the effective extremal entropy $S_{0,\text{eff}}$ has the form of counting the states of these branes.

Figures (23)

• Figure 1: The phase diagram of matrix model of JT gravity with $K$ flavors of EOW branes. Green region is "Y" shaped phase, blue region is one-cut phase and red curve is critical line.
• Figure 2: The solution of JT gravity. The light green region is physical in which $\Phi+\phi_{0}\geq0$. Red curves are two AdS boundaries with $T\in[-\pi/2,\pi/2]$. The dashed lines are horizon. Blue curve is the geodesic of EOW brane.
• Figure 3: The partition function $Z(\beta)$ in which all genera and EOW brane loops are summed. Red curve is AdS boundary and blue curves are EOW branes.
• Figure 4: The plot of $\sqrt{u}I_{1}(2\pi\sqrt{u})$ as a function of $u$.
• Figure 5: Plot of $\sqrt{x}I_1(2\pi\sqrt{x})/(2\pi)$ (blue) and $-Ke^{-S_0}f_\lambda(x)$ (other colors) for different $\lambda$. The largest intersection point gives zero point energy $E_0$. (a) yellow, green and red means increasing $K$ and $E_0$ moves rightward as $K$ increases; (b) yellow is $K<K_{cr}^=$, green is critical $K=K_{cr}^=$ and red is $K>K_{cr}^=$. $E_0=0$ when $K\leq K_{cr}^=$, and $E_0>0$ when $K>K_{cr}^=$; (c) yellow is $K>K_{cr}^>$, green is critical $K=K_{cr}^>$, red is $K<K_{cr}^>$ and purple is for $K$ too large such that no intersection exists (this purple curve also has smaller $\mu$ than the other three). $E_0$ moves leftward when $K$ increases and has a jump when $K>K_{cr}^>$. In the plot, we set $2\phi_b =1$ and $e^{S_0}=1$.