Structure of deformations in Jackiw-Teitelboim black holes with matter

TL;DR

This paper studies how matter-induced deformations affect the structure of Jackiw-Teitelboim black holes, revealing insights into bulk-boundary relations and potential behind-horizon degrees of freedom.

Contribution

It explicitly constructs the Hilbert space and operator basis for matter deformations in JT gravity, including higher-order corrections and their implications.

Findings

Deformed thermofield double states are realized via operator insertions.

Inserted operators form an SL(2, R) representation.

Bulk geometry becomes asymmetric with higher-order corrections.

Abstract

We consider Jackiw-Teitelboim gravity with a massless matter field and turn on bulk excitations leading to a nontrivial vev of the corresponding dual boundary operator. To leading order, we realize the corresponding deformation of thermofield double state by explicitly identifying their Hilbert space. The deformed state can be prepared with an operator insertion at the mid-point of the Euclidean time evolution in the context of Hartle-Hawking construction. We show that the inserted operators form an SL(2,{\bf R}) representation. We construct a specific orthonormal basis that is directly related to the operator basis of the vev deformations. If we include the higher order corrections, the bulk geometry is no longer left-right symmetric. We argue that, classically, the mode coefficients in the bulk deformation cannot be fully recovered from the data collected along the boundary cutoff trajectories. Then the bulk seems to contain more information than the cutoff boundary, and this might be responsible for nontrivial behind-horizon degrees of freedom.