The Schwarzian Theory - A Wilson Line Perspective

TL;DR

This paper offers a holographic interpretation of Schwarzian quantum mechanics through Wilson line correlators in Jackiw-Teitelboim gravity, connecting boundary correlators with bulk Wilson line diagrams and deriving Schwarzian correlators.

Contribution

It introduces a Wilson line perspective on Schwarzian theory, linking boundary correlators to bulk BF theory and deriving out-of-time ordered correlators using crossing Wilson lines.

Findings

Wilson line correlators represent bilocal correlators in particle-on-a-group models.

Derived Schwarzian correlation functions from SL(2,R) Hamiltonian reduction.

Out-of-time ordered correlators correspond to crossing Wilson lines, matching 2d CFT results.

Abstract

We provide a holographic perspective on correlation functions in Schwarzian quantum mechanics, as boundary-anchored Wilson line correlators in Jackiw-Teitelboim gravity. We first study compact groups and identify the diagrammatic representation of bilocal correlators of the particle-on-a-group model as Wilson line correlators in its 2d holographic BF description. We generalize to the Hamiltonian reduction of SL(2,R) and derive the Schwarzian correlation functions. Out-of-time ordered correlators are determined by crossing Wilson lines, giving a 6j-symbol, in agreement with 2d CFT results.