One-dimensional Quantum Gravity and the Schwarzian theory

Understand

We develop a model of one-dimensional (Conformal) Quantum Gravity.

• By discussing the connection between Goldstone and Gauge theories, we establish that this model effectively computes the partition function of the Schwarzian theory where the $\textrm{SL}(2,\mathbb{R})$ symmetry is realized on the base space.
• The computation is straightforward, involves a local quantum measure and does not rely on localization arguments.
• Non-localities in the model are exclusively related to the value of fixed gauge invariant moduli.