A universe field theory for JT gravity

TL;DR

<3-5 sentence high-level summary>The paper develops a universe field theory for JT gravity by identifying a two-dimensional Kodaira-Spencer theory on the JT spectral curve as the field theory of baby universes. It shows that the perturbative expansion of the KS theory reproduces the gravitational path integral over topologies, with the disk, annulus, and higher-genus JT amplitudes arising from KS correlators via an inverse Laplace transform, and it recasts the JT/matrix-model correspondence as an open/closed duality in topological string theory. Non-perturbative effects are captured by non-compact D-branes and Z2-twisted fermions in the KS description, yielding the universal sine-kernel in spectral correlators and providing a concrete non-perturbative completion of JT gravity. The framework links ensemble averages to KS open-string sectors, offers a route to α-states and baby-universe Hilbert spaces, and suggests extensions to super JT gravity, deformations, and higher-dimensional gravity via similar topological-string-inspired structures.

Abstract

We present a field theory description for the non-perturbative splitting and joining of baby universes in Euclidean Jackiw-Teitelboim (JT) gravity. We show how the gravitational path integral, defined as a sum over topologies, can be reproduced from the perturbative expansion of a Kodaira-Spencer (KS) field theory for the complex structure deformations of the spectral curve. We use that the Schwinger-Dyson equations for the KS theory can be mapped to the topological recursion relations. We refer to this dual description of JT gravity as a `universe field theory'. By introducing non-compact D-branes in the target space geometry, we can probe non-perturbative aspects of JT gravity. The relevant operators are obtained through a modification of the JT path integral with Neumann boundary conditions. The KS/JT identification suggests that the ensemble average for JT gravity can be understood in terms of a more standard open/closed duality in topological string theory.

Figures (14)

• Figure 1: A triangle of relations between JT, KS and MM, together with their interpretation in topological string theory.
• Figure 2: Fixing the behaviour of $\omega$ at $\infty$ determines the classical value $\partial\Phi_{cl}$. As one moves away from infinity, quantum fluctuations of $\partial\Phi$ can appear which deform the complex structure. At the contour $\gamma$ there is a coordinate change to the patch that covers $0$.
• Figure 3: The disk (a) and annulus (b) geometries in JT gravity. The blue line represents the 'wiggles' due to the boundary dynamics of the Schwarzian theory.
• Figure 4: A pictorial representation of non-compact D-brane insertions on the spectral curve $\mathcal{S}$. The straight lines correspond to the non-compact fiber directions $u=0$ or $v=0$ which are wrapped by branes $\psi$ and anti-branes $\psi^{\dagger}$ respectively, having opposite flux as indicated by the direction of the arrow. The branch cut is denoted by a red wiggly line.
• Figure 5: The creation of DD and DN boundary trumpets $Z(\beta)$ and $Z(E)$ in JT gravity, indicated by blue and yellow boundaries respectively.