Momentum in single-trace TT¯ holography

We continue our exploration of the holographic duality between string theory in backgrounds that interpolate between asymptotically linear dilaton spacetime in the UV and AdS₃ in the IR, and the corresponding boundary theories. In previous papers, [1], [2], we showed that states in the bulk theory that are described by non-trivial asymptotically linear dilaton geometries, such as black holes and deformed global AdS₃, can be described in the boundary theory by a single-trace TT¯ deformation of a symmetric product theory. In those papers, we restricted to states with vanishing (angular) momentum; in this paper, we extend the analysis to states with arbitrary momentum, and show that the picture presented in the earlier papers generalizes to this case.