KdV charges in TTbar theories and new models with super-Hagedorn behavior

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} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo accent="true">‾</mml:mo> </mml:mover> </mml:mrow> </mml:math> deformation and its generalizations. We determine the flow equations the KdV charges obey under the T\bar{T} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo accent="true">‾</mml:mo> </mml:mover> </mml:mrow> </mml:math> deformation: they behave as probes “riding the Burgers flow” of the energy eigenvalues. We also study a Lorentz-breaking T_{s+1}\bar{T} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mover> <mml:mi>T</mml:mi> <mml:mo accent="true">‾</mml:mo> </mml:mover> </mml:mrow> </mml:math> deformation built from a KdV current and the stress tensor, and find a super-Hagedorn growth of the density of states.