# Relative entropy for coherent states in chiral CFT

## TL;DR

This paper establishes a connection between the relative entropy of certain states in chiral CFT and the Schwarzian action of associated diffeomorphisms, providing explicit formulas and applications to solitonic states.

## Contribution

It demonstrates that the relative entropy in chiral CFT equals the Schwarzian action scaled by the central charge, linking quantum information measures to geometric actions.

## Key findings

- Relative entropy equals c times the Schwarzian action of the diffeomorphism.
- Derived a formula for the relative entropy between vacuum and solitonic states.
- Established a geometric interpretation of relative entropy in chiral CFT.

## Abstract

We consider the relative entropy between the vacuum state and a state obtained by applying an exponentiated stress tensor to the vacuum of a chiral conformal field theory on the lightray. The smearing function of the stress tensor can be viewed as a vector field on the real line generating a diffeomorphism. We show that the relative entropy is equal to $c$ times the so-called Schwarzian action of the diffeomorphism. As an application of this result, we obtain a formula for the relative entropy between the vacuum and a solitonic state.