# Quantum Correction to Chaos in Schwarzian Theory

## TL;DR

This paper analyzes quantum corrections to chaos in Schwarzian theory, showing that soft mode quantum effects reduce the maximal Lyapunov exponent, with detailed semi-classical Feynman diagram calculations up to fourth order.

## Contribution

It provides a semi-classical analysis of quantum effects on chaos in Schwarzian theory, specifically calculating soft mode contributions to out-of-time-order correlators up to order g^4.

## Key findings

- Quantum correction decreases the Lyapunov exponent from its classical maximum
- Soft mode contributions are explicitly calculated up to order g^4
- Quantum effects soften chaos in Schwarzian theory

## Abstract

We discuss the quantum correction to chaos in the Schwarzian theory. We carry out the semi-classical analysis of the Schwarzian theory to study Feynman diagrams of the Schwarzian soft mode. We evaluate the contribution of the soft mode to the out-of-time-order correlator up to order $\mathcal{O}(g^4)$. We show that the quantum correction of order $\mathcal{O}(g^4)$ by the soft mode decreases the maximum Lyapunov exponent $2\pi/ \beta$.