# Fermionic Localization of the Schwarzian Theory

## TL;DR

This paper demonstrates that the path integral of the Schwarzian theory, related to the SYK model and quantum black holes, is exactly solvable using fermionic localization techniques despite being a bosonic model.

## Contribution

It introduces a novel fermionic localization method to exactly evaluate the Schwarzian path integral, revealing new computational insights.

## Key findings

- Path integral is one-loop exact.
- Fermionic localization applies to a bosonic model.
- Provides a new analytical tool for Schwarzian theory.

## Abstract

The SYK model is a quantum mechanical model that has been proposed to be holographically dual to a $1+1$-dimensional model of a quantum black hole. An emergent "gravitational" mode of this model is governed by an unusual action that that has been called the Schwarzian action. It governs a reparametrization of a circle. We show that the path integral of the Schwarzian theory is one-loop exact. The argument uses a method of fermionic localization, even though the model itself is purely bosonic.