Entanglement Entropy for $TT$ deformed CFT in general dimensions

TL;DR

The paper extends the solvable TT-like deformation to higher dimensions via the X_d operator, studying large-N CFTs on S^d and its holographic dual in AdS_{d+1} with a hard radial cut-off. It derives the exact sphere partition function and field-theory entanglement entropy, and validates these against holographic Ryu–Takayanagi computations, including a consistent renormalized entanglement entropy (REE) framework. Across dimensions d=2–6, EE is finite and its universal components align between field theory and holography, with REE providing a UV-finite, scheme-consistent measure that interpolates between the IR CFT data and vanishing UV entanglement. These results reinforce the higher-dimensional TT deformation as a controlled holographic setup and illuminate RG-flow behavior and potential connections to the surface/state correspondence.

Abstract

We consider deformation of a generic $d$ dimensional ($d\geq 2$) large-$N$ CFT on a sphere by a spin-0 operator which is bilinear in the components of the stress tensor. Such a deformation has been proposed to be holographically dual to an $AdS_{d+1}$ bulk with a hard radial cut-off. We compute the exact partition function and find the entanglement entropy from the field theory side in various dimensions and compare with the corresponding holographic results. We also compute renormalized entanglement entropy both in field theory and holography and find complete agreement between them.