Generalized conformal quantum mechanics as an ideal observer in two-dimensional gravity

TL;DR

This paper derives a generalized conformal mechanics model coupled to JT gravity from black hole near-horizon physics, exploring its classical and quantum properties and its potential as an ideal observer in quantum gravity.

Contribution

It introduces a new GCM-JT gravity model from black hole physics and analyzes its classical and quantum solutions, providing a framework for a solvable quantum gravity detector.

Findings

Backreaction of the wavefunction vanishes in classical approximation.

Time-reparametrization mode can be inferred from observables.

The full theory is quantizable and solvable.

Abstract

We obtain an action for a generalized conformal mechanics (GCM) coupled to Jackiw-Teitelboim (JT) gravity from a double scaling limit of the motion of a charged massive particle in the near-horizon geometry of a near-extremal spherical black hole. When JT gravity is treated in the classical approximation, the backreaction of the particle's wavefunction on the time-reparametrization mode (and therefore the bulk metric) vanishes while the conformal symmetry in GCM is reparametrized in a state-dependent way. We also construct the semi-classical Hilbert space of the full theory by explicitly solving the general time-dependent normalizable solutions of the Schr\"{o}dinger equation for GCM, and show that the time-reparametrization mode can be inferred from the measurement of suitable observables. Since the full theory of the GCM coupled to JT gravity is amenable to quantization, it can lead to a solvable model for a detector coupled to quantum gravity.