Jackiw-Teitelboim Model Coupled to Conformal Matter in the Semi-Classical Limit

TL;DR

This work analyzes the Jackiw-Teitelboim model of 2D gravity coupled to conformal matter in the semiclassical regime. By comparing two boundary-condition–driven realizations—the nonminimally coupled χ system and the minimally coupled ψ system—the authors uncover distinct thermodynamic responses, relaxation dynamics, and horizon entropies. They introduce a generalized entropy that combines horizon dilaton contributions with matter entanglement and prove a second-law-like monotonicity for both the event horizon and future Q-screens under appropriate energy conditions. The results illuminate how boundary conditions shape quantum backreaction and horizon thermodynamics in JT gravity, offering insights into holography, quantum focusing, and the role of entanglement in low-dimensional gravity.

Abstract

We analyse the Jackiw-Teitelboim model of 2D gravity coupled to $N$ massless free scalar fields in the semi-classical limit. Two systems are studied which essentially differ in the boundary conditions that are imposed. We find that the thermodynamics has interesting differences. We also analyse the response to additional infalling matter which satisfies the null energy condition. The second law is shown to be valid in both systems for the generalised entropy which takes into account the entanglement across the event horizon due to the matter fields. Similarly we find that the generalised entropy increases along future Q-screens in both systems.

Figures (1)

• Figure 1: Entanglement of matter fields across the horizon