Canonical maps and integrability in $T\bar T$ deformed 2d CFTs

Understand

We study $T\bar T$ deformations of 2d CFTs with periodic boundary conditions.

• We relate these systems to string models on $\mathbb{R}\times {S}^1\times{\cal M}$, where $\cal M$ is the target space of a 2d CFT.
• The string model in the light cone gauge is identified with the corresponding 2d CFT and in the static gauge it reproduces its $T\bar T$ deformed system.
• This relates the deformed system and the initial one by a worldsheet coordinate transformation, which becomes a time dependent canonical map in the Hamiltonian treatment.