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.
Categories: hep-th