Genus-Two Contributions to Late-Time Correlators in JT Gravity

Abstract

In this work, we analyze the late-time two-point correlation function in Jackiw--Teitelboim gravity, focusing on the genus-two ($g=2$) contribution associated with two baby universes. Extending the analysis of the single-baby-universe ($g=1$) case, we formulate an amplitude describing the emission and absorption of two baby universes during the evolution of the Hartle--Hawking state. This formulation reduces the problem to a moduli-space integral involving the Weil--Petersson volume $V_{0,3}$. To evaluate this integral, we decompose $V_{0,3}$ into contributions from Kontsevich graphs and extend the no-shortcut condition to the relevant genus-two strip geometries. Combined with the strip approximation, this decomposition reorganizes the moduli-space integral into a finite sum of contributions associated with distinct geometric configurations. We then explicitly evaluate the strip-geometry contributions corresponding to the emission of two baby universes and determine their contribution to the genus-two late-time two-point correlation function. Our results suggest that the strip approximation, together with the no-shortcut condition, provides a useful analytic framework for studying higher-genus geometries containing multiple wormholes.

24page,11figure