# KdV charges in $T\bar{T}$ theories and new models with super-Hagedorn behavior

## TL;DR

This paper investigates how KdV charges in 2D CFTs and integrable models evolve under $T\bar{T}$ deformations, revealing their behavior as probes of energy flow and discovering models with super-Hagedorn density growth.

## Contribution

It derives flow equations for KdV charges under $T\bar{T}$ deformation and introduces a Lorentz-breaking deformation leading to super-Hagedorn behavior.

## Key findings

- KdV charges obey Burgers flow equations under deformation.
- $T\bar{T}$ deformation preserves KdV charge conservation.
- Lorentz-breaking deformation results in super-Hagedorn density of states.

## Abstract

Two-dimensional CFTs and integrable models have an infinite set of conserved KdV higher spin currents. These currents can be argued to remain conserved under the $T\bar{T}$ deformation and its generalizations. We determine the flow equations the KdV charges obey under the $T\bar{T}$ deformation: they behave as probes "riding the Burgers flow" of the energy eigenvalues. We also study a Lorentz-breaking $T_{s+1}\bar{T}$ deformation built from a KdV current and the stress tensor, and find a super-Hagedorn growth of the density of states.