Quantum mechanics

Theoretical physics

Wilson loop

Pure mathematics

Mathematical physics

Mathematical optimization

Hamiltonian (control theory)

Gauge theory

Physics

Mathematics

Representation theory

Mathematical analysis

Geometry

Schwarzian derivative

Perspective (graphical)

Real line

Line (geometry)

Journal of High Energy Physics

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.

The Schwarzian theory — a Wilson line perspective