An exact quantization of Jackiw-Teitelboim gravity

TL;DR

The paper presents an exact quantization of 2D JT gravity by recasting it as a 2D BF theory with a central-extension gauge group G_B of PSL(2,R) by R and a boundary loop defect that enforces Schwarzian boundary dynamics. The authors compute the disk partition function and prove a precise match with the Schwarzian finite-temperature partition function, and establish a detailed dictionary between boundary-anchored Wilson lines and Schwarzian bi-local operators, with Wilson lines corresponding to bulk particle worldlines in AdS2 JT gravity. They develop a representation-theoretic framework for non-compact groups, isolating the principal series via boundary conditions and a large-B limit to reproduce Schwarzian observables, and they derive diagrammatic rules using fusion and 6-j symbols to compute correlators of bilocals, including OTOCs and intersecting configurations. This work provides a concrete holographic dictionary in 2D, enabling exact bulk calculations and opening routes to generalizations to other gauge choices, deformations, and Lorentzian/dS contexts.

Abstract

We propose an exact quantization of two-dimensional Jackiw-Teitelboim (JT) gravity by formulating the JT gravity theory as a 2D gauge theory placed in the presence of a loop defect. The gauge group is a certain central extension of $PSL(2, \mathbb{R})$ by $\mathbb{R}$. We find that the exact partition function of our theory when placed on a Euclidean disk matches precisely the finite temperature partition function of the Schwarzian theory. We show that observables on both sides are also precisely matched: correlation functions of boundary-anchored Wilson lines in the bulk are given by those of bi-local operators in the Schwarzian theory. In the gravitational context, the Wilson lines are shown to be equivalent to the world-lines of massive particles in the metric formulation of JT gravity.

Figures (5)

• Figure 1: Schematic representation showing that the dynamics on the defect in the gauge theory is the same as that in the Schwarzian theory, which in turn describes the boundary degrees of freedom of \ref{['eq:JT-gravity-action']}.
• Figure 2: Cartoon emphasizing the properties of the string defect. The resulting theory is invariant under perimeter preserving defect diffeomorphisms and thus the defect can be brought arbitrarily close to the boundary of the manifold. Furthermore, the degrees of freedom of the gauge theory defect can be captured by those in the Schwarzian theory.
• Figure 3: Cartoon showing an example of gluing of three disk patches whose overall partition function is given by the gluing rules in \ref{['eq:gluing-rules']}. Each segment has an associated group element $h_a$ and each patch has an associated holonomy $g_i$. In the case pictured above: $g_1 = h_1h_2 h_3^{-1}$, $g_2= h_3 h_4 h_5^{-1}$ and $g_3 = h_5 h_6 h_1^{-1}$. We take all edges to be oriented in the counter-clockwise direction.
• Figure 4: Several Euclidean Wilson line configurations, equivalent to different finite temperature correlation functions of the bi-local operator $\mathcal{O}_\lambda(x_1, x_2)$: the top-left figure shows $\langle \mathcal{O}_\lambda(\tau_1, \tau_2) \rangle_\beta = \langle \mathcal{W}_\lambda(\mathcal{C}_{\tau_1, \tau_2}) \rangle$, the top-right figure yields the equality of the time-ordered correlators $\langle \mathcal{O}_{\lambda_1}(\tau_1, \tau_2) \mathcal{O}_{\lambda_2}(\tau_3, \tau_4)\rangle_\beta = \langle \mathcal{W}_{\lambda_1}(\mathcal{C}_{\tau_1, \tau_2}) \mathcal{W}_{\lambda_2}(\mathcal{C}_{\tau_3, \tau_4}) \rangle$, the bottom-left figure shows a pair of intersecting Wilson lines that can be disentangled to the top-right configuration, while the bottom-right figure gives the out-of-time-ordered configurations. Note that the results are independent of the trajectory of the Wilson line inside of the bulk and only depend on the location where the Wilson lines intersect the defect.
• Figure 5: An example of a three-particle bulk interaction vertex corresponding to the junction of three Wilson lines defined by a Clebsch-Gordan coefficient at the vertex.