Rotating strings and anomalous dimensions in Non-AdS holography

In this paper we consider certain rigidly rotating closed string configurations in an asymptotically non-AdS string background. The string background is a deformation of AdS₃ × M₇. It interpolates between AdS₃ and asymptotically linear dilaton I\!R × S¹ × I\!R spacetime (times the internal compact manifold M₇). We compute the quantity $E - J$ (in the large J limit) where E is the energy and J is the angular momentum of the spinning strings. In the two dimensional CFT dual to string theory on AdS₃ (times M₇) it gives the anomalous dimensions of certain twist two and higher operators. We show in the deformed background that $E - J$ is bounded. At a special value of the deformation coupling we also show that for spinning closed strings containing $n > 2$ cusps or spikes both E and J are bounded. In the CFT dual to string theory on AdS₃ (times M₇) the spinning cusped strings describe operators with twist n larger than two. In general, at other values of the deformation coupling, we demonstrate that this feature is exhibited only by those cusped strings with n > n₀ where n₀ is determined only by the deformation coupling. We also give simple exact Regge relations between E and J. We also study the closely related cusp anomalous dimension of a light-like Wilson loop. We comment on what $E - J$ measures away from the CFT along the deformation in the coupling space. In the long string sector the deformation is dual to a single trace T T deformed orbifold theory. We determine the associated deformed sinh-Gordon model that classically describes the (long) strings near the boundary. This provides an example of single trace T T deformation in non-orbifold theories.