# Defects in Jackiw-Teitelboim Quantum Gravity

## TL;DR

This paper classifies and analyzes defects in 2D Jackiw-Teitelboim gravity, linking them to deformations of the Schwarzian theory, and explores their quantization, geometric observables, and connections to Liouville CFT and SYK models.

## Contribution

It introduces a novel classification of defects in JT gravity via coadjoint orbits and relates these to Liouville CFT and deformations of the Schwarzian theory.

## Key findings

- Quantization of coadjoint orbits relates to Liouville CFT with branes and Verlinde operators.
- Partition functions and correlators for deformed Schwarzian theories are computed.
- Application to low-energy complex SYK with U(1) symmetry and non-abelian generalization.

## Abstract

We classify and study defects in 2d Jackiw-Teitelboim gravity. We show these are holographically described by a deformation of the Schwarzian theory where the reparametrization mode is integrated over different coadjoint orbits of the Virasoro group. We show that the quantization of each coadjoint orbit is connected to 2d Liouville CFT between branes with insertions of Verlinde loop operators. We also propose an interpretation for the exceptional orbits. We use this perspective to solve these deformations of the Schwarzian theory, computing their partition function and correlators. In the process, we define two geometric observables: the horizon area operator $\Phi_h$ and the geodesic length operator $L(\gamma)$. We show this procedure is structurally related to the deformation of the particle-on-a-group quantum mechanics by the addition of a chemical potential. As an example, we solve the low-energy theory of complex SYK with a U(1) symmetry and generalize to the non-abelian case.