Moving holographic boundaries

In this paper, we show that for one sign of the deformation coupling single-trace $T{\bar T}$ deformation moves the holographic screen in G\"{o}del universe radially inward. For the other sign of the coupling it moves the holographic screen radially outward. We (thus) argue, on general grounds, that in holography (single-trace) $T{\bar T}$ deformation can be generally thought of as either moving the holographic boundary into the bulk or washing it away to infinity. In Anti-de Sitter this breaks the spacetime conformal symmetry. We further note that moving timelike holographic boundary into bulk creates a curvature singularity. In the boundary the singularity is understood by states with imaginary energies. To make the theory sensible we introduce an ultraviolet cutoff and thereby move the boundary into the bulk. In this paper we first obtain the Penrose limit of the single-trace $T{\bar T}$ deformed string background and then perform $T$-duality along a space-like isometry to obtain a class of (deformed) G\"{o}del universes. The string background we consider is $AdS_3\times S^3\times {\cal M}_4$. The single-trace $T{\bar T}$ deformation is a particular example of the more general $O(d, d)$ transformations.