Entanglement Entropy and T(T)over-bar Deformation

Quantum gravity in a finite region of spacetime is conjectured to be dual to a conformal field theory (CFT) deformed by the irrelevant operator T (T) over bar. We test this conjecture with entanglement entropy, which is sensitive to ultraviolet physics on the boundary, while also probing the bulk geometry. We find that the entanglement entropy for an entangling surface consisting of two antipodal points on a sphere is finite and precisely matches the Ryu-Takayanagi formula applied to a finite region consistent with the conjecture of McGough et al. We also consider a one-parameter family of conical entropies, which are finite and verify a conjecture due to Dong. Since ultraviolet divergences are local, we conclude that the T (T) over bar deformation acts as an ultraviolet cutoff on the entanglement entropy. Our results support the conjecture that the T (T) over bar -deformed CFT is the holographic dual of a finite region of spacetime.