Comments on Lorentzian topology change in JT gravity

TL;DR

This paper introduces a Lorentzian path integral formulation for JT gravity that incorporates topology-changing configurations, inspired by string theory techniques, and relates Euclidean and Lorentzian amplitudes.

Contribution

It provides a novel definition of the Lorentzian JT gravity path integral including topology change, inspired by bosonic string genus expansion and lightcone diagrams.

Findings

Defines Lorentzian JT path integral with topology change

Connects Euclidean and Lorentzian JT amplitudes

Uses analytic continuation from Euclidean to Lorentzian

Abstract

We propose a definition for the Lorentzian Jackiw-Teitelboim (JT) gravity path integral that includes Lorentzian topology changing configurations. The construction is inspired by the bosonic string genus expansion on singular Lorentzian worldsheets, with geometries known as lightcone diagrams playing a prominent role. The Lorentzian path integral is defined through a suitable analytic continuation of the Euclidean path integral, and includes metrics that become degenerate at isolated points allowing for Lorentzian topology changing transitions. We discuss the relation between Euclidean JT amplitudes and the proposed Lorentzian amplitudes.