$T\bar{T}$, $J\bar{T}$, $T\bar{J}$ and String Theory

Understand

We calculate the spectrum of a two dimensional CFT on a cylinder, perturbed by a general linear combination of $T\bar{T}$, $J\bar{T}$ and $T\bar{J}$, by utilizing the relation of this problem to certain solvable single trace current-current deformations of the worldsheet theory of strings on $AdS_3$.

• We show that this spectrum is well behaved (i.e.
• the energies are real) if and only if the dual bulk geometry is well behaved (i.e.
• the signature of the bulk spacetime is $(1,2)$ and there are no closed timelike curves).