# On KdV characters in large c CFTs

## TL;DR

This paper explores the integrable structure of large central charge 2D CFTs, relating their charges to quantum Sinh-Gordon theory, and analyzes the growth and properties of their characters in the large c limit.

## Contribution

It explicitly calculates single charge characters at large c, revealing their degeneracy growth and approximation methods for small chemical potentials, connecting CFT charges to Sinh-Gordon theory.

## Key findings

- Degeneracy growth of characters within modules
- Approximate character behavior at small chemical potential
- Insights into transformation properties of characters

## Abstract

Two-dimensional conformal field theories with just Virasoro symmetry are endowed with integrable structure. We review how to construct the integrable charges in a two-dimensional conformal field theory and how to relate them to the charges of quantum Sinh-Gordon theory when c>25. We then explicitly calculate the single charge characters in the large c limit for all charges and thereby reveal how their degeneracies grow within one module. This, in particular, allows us to approximate the characters in the limit of small chemical potential, which source the respective charges. The latter give us insights into possible transformation properties of the characters. We also comment on the full generalized Gibbs ensemble and approximations to pure states.