The Microstate Physics of JT Gravity and Supergravity

TL;DR

The paper argues that fully non-perturbative double-scaled matrix models provide a unified view of 2D gravity, showing a discrete microstate spectrum that underlies the Schwarzian limit and indicating a single holographic dual for JT gravity and its supersymmetric variants. By blending Wignerian spectral data with 't Hooft topological expansions, it demonstrates that Euclidean gravity sums correspond to ensemble averages over discrete spectra, while Lorentzian holography corresponds to a single, well-defined spectrum characterized by peaks at energies ${\cal E}_n$ and encoded in objects like the Fredholm determinant and D-brane wavefunctions. The work develops a robust framework— Dyson gas dynamics, a one-dimensional quantum-mechanical problem with Hamiltonian ${\mathcal H}=-\hbar^2\partial_x^2+u(x)$, and a matrix-model kernel $K(E,E')$—to extract microstate information from non-perturbative data and to compute thermodynamic and dynamical quantities (free energies, spectral form factors) in both JT gravity and JT supergravity. These results suggest that gravity is not fundamentally an ensemble, but that ensemble methods in the Euclidean sector efficiently illuminate holographic duals via a discrete spectrum, with broad implications for interpreting Euclidean gravity sums and for extending holography to higher dimensions.

Abstract

It is proposed that a complete understanding of two-dimensional quantum gravity and its emergence in random matrix models requires fully embracing {\it both} Wigner (statistics) and 't Hooft (geometry). Using non-perturbative definitions of random matrix models that yield various JT gravity and JT supergravity models on Euclidean surfaces of arbitrary topology, Fredholm determinants are used to extract precise information about the spectra of discrete microstates that underlie the physics. A core result of the computations is that in each case, the (super) Schwarzian spectrum seen at leading order is only an approximation to a new kind of spectrum that is fundamentally discrete. It is further argued that the matrix models point to a {\it single} distinguished copy of the discrete spectrum that characterizes the holographic dual of the Lorentzian (super) gravity theory. These facts suggest that the factorization puzzle is entirely resolved since the discrete spectrum underlying the Schwarzian can have a sensible quantum mechanical origin in a single theory, without an appeal to an ensemble. It is argued that more generally, double-scaled matrix models contain information about both the Lorentzian and Euclidean approaches to quantum gravity. The former comes from the Wignerian approach while the latter from the 't Hooftian 1/N topological expansion.

Figures (39)

• Figure 1: An example of JT gravity's first 150 microstates, denoted as the set $\{{\cal E}_n\}$ in the text. ($\hbar{=}1$).
• Figure 2: A schematic layout of the paths to finding the dual spectrum. The top path is four-dimensional, and Lorentzian. The bottom is two dimensional, and Euclidean. A Wignerian approach to the top path would study the ensemble of Hamiltonians with the correct asymptotic fixed by the Schwarzian result (see a remark in footnote \ref{['fn:lorentzian-subtleties']}), reading off the likely properties of the full spectrum at the end. This is a random matrix model. A 't Hooftian expansion of that same matrix model gives a topological expansion that coincides (as it must) with 2D Euclidean JT gravity and the perturbative matrix model of ref. Saad:2019lba.
• Figure 3: The full spectral density $\rho(E)$ (solid black) for a non-perturbative completion of JT gravity, the leading disc result $\rho_0(E)$ (dashed), and the semi-classical estimate $\rho_{\rm sc}(E)$ (red, dash-dot). Here $\hbar{=}1$.
• Figure 4: Full spectral density $\rho(E)$ (solid black), leading density $\rho_{_0}\!(E)$ (blue dashed), and probability densities (also cumulative probabilities, dashed) of the first 6 states of the JT gravity microstate spectrum. ($s$ is another name for $E$ that will be explained later.) Inset: Close-up of $\rho(E)$ and distributions for the ground state, with ${\cal E}_0{\equiv}\langle E_0\rangle{\simeq}0.663$. Note that $\hbar{=}{\rm e}^{-S_0}{=}1$ here.
• Figure 5: A sketch of low vs. high energy regimes with the full spectral density $\rho(E)$ (solid black). The blue curves, whose sum gives $\rho(E)$, are the underlying microstate peak probability densities. In the high energy scenario A (right), for a given $\delta E$, $\rho(E)$ captures more contributions from typical configurations than in the low energy scenario B (left).