Strings in irrelevant deformations of AdS₃ /CFT₂

We generalize our recent analysis [1] of probe string dynamics to the case of general single-trace TT¯ , JT¯ and TJ¯ deformations. We show that in regions in coupling space where the bulk geometry is smooth, the classical trajectories of such strings are smooth and approach the linear dilaton boundary at either the far past or the far future. These trajectories give rise to quantum scattering states with arbitrarily high energies. When the bulk geometry has closed timelike curves (CTC’s), the trajectories are singular for energies above a critical value E_c. This singularity occurs in the region with CTC’s, and the value of E_c agrees with that read off from the dual boundary theory for all values of the couplings and charges.