Dilaton-gravity, deformations of the minimal string, and matrix models

TL;DR

The work establishes a holographic link between two-dimensional dilaton-gravity in AdS$_2$ and matrix-model ensembles, extending JT gravity by including conical defects through the large-$p$ limit of deformed $(2,p)$ minimal string theory. By translating defect data into a defect-generating function $W(y)$ and into dilaton-potentials $U(\Phi)$, the authors derive an exact disk density of states for JT gravity with general defects and relate these results to a 2D dilaton-gravity framework with polynomial-like potentials. The Belavin–Zamolodchikov string equation plays a central role, enabling a precise map between tachyon deformations in the minimal string and defect insertions in JT gravity, including merging phenomena for blunt defects ($\alpha>1/2$). The findings provide a robust, semiclassically controlled route to constructing and solving dilaton-gravity theories with nontrivial potentials, with potential implications for understanding ensemble gravity and holography beyond pure JT. Overall, the paper delivers a coherent, exact approach to deformations of JT gravity via minimal-string dualities and highlights practical pathways to polynomial dilaton potentials in 2D gravity.

Abstract

A large class of two-dimensional dilaton-gravity theories in asymptotically AdS$_2$ spacetimes are holographically dual to a matrix integral, interpreted as an ensemble average over Hamiltonians. Viewing these theories as Jackiw-Teitelboim gravity with a gas of defects, we extend this duality to a broader class of dilaton potentials compared to previous work by including conical defects with small deficit angles. In order to do this we show that these theories are equal to the large $p$ limit of a natural deformation of the $(2,p)$ minimal string theory.

Figures (6)

• Figure 1: Relation between the three theories we are interested in and their respective deformations: the minimal string, time-like Liouville coupled to space-like Liouville and JT gravity with defects. The connection between the $(2,p)$ minimal string and the combination of Liouville theories is the least rigorous since it relies on a Coulomb gas representation of the minimal model.
• Figure 2: Left: The SSS construction of the correlator $\langle Z(\beta_1) Z(\beta_2) Z(\beta_3) \rangle_C$. The Weil-Petersson volume $V_{g=0,n=3}$ is glued to trumpets along each of the three geodesic boundaries. Right: Analogous construction of the correlator with sharp conical defects. The Weil-Petersson volume $V_{g=0,n=3,k=3}$ has three sharp defects.
• Figure 3: Left: Picture of a hyperbolic surface with a holographic boundary to the left and two sharp defects shown to the right with $\alpha<1/2$. In dashed line we show a geodesic homologous to the holographic boundary. Right: Similar picture of a hyperbolic surface in the case $\alpha>1/2$. As argued in the main text there is no geodesic to cut and glue.
• Figure 4: The relationship between the minimal string operators $\mathcal{T}_{n}$ and the JT defect parameter $\alpha$. The spacing between the operators in $\alpha$ is discrete and of order $1/p$; as we take the JT limit by sending $p$ to infinity, $\alpha$ becomes a continuous parameter.
• Figure 5: We illustrate the geometry for the quadratic deformation constructed in section \ref{['sec:PolyPotentials']}. The blue curve corresponds to the Schwarzian boundary, while the shaded region corresponds to the portion of the disk where the deformation to the dilaton potential is approximately quadratic. The region in between corresponds to the transition from the nearly polynomial behavior to AdS$_2$ asymptotics.