Comments on holographic entanglements in cutoff AdS
Toshihiro Ota
TL;DR
The paper addresses how an irrelevant TT deformation affects holographic entanglement structures in a cutoff AdS/CFT setup. It analyzes two-interval holographic entanglement entropy and entanglement of purification by computing geodesic lengths and entanglement wedge cross sections in cutoff AdS, introducing the finite radial cutoff $z_c=\sqrt{\frac{\mu c}{24\pi}}$. The main findings are that TT deformation acts as an energy-scale rescaling, causing the two-interval transition point to shift toward smaller subintervals and reducing the entanglement wedge cross section for small deformations, with temperature-dependent transitions at fixed subsystems in BTZ backgrounds. These results provide holographic predictions for entanglement in $T\bar{T}$-deformed CFTs and offer insight into bulk locality and thermo-field dynamics under a finite cutoff.
Abstract
We study two-interval holographic entanglement entropy and entanglement wedge cross section in cutoff AdS. In particular, we investigate phase transitions of them. For two-interval entanglement entropy, the transition point monotonically decreases with a deformation parameter, which means that by the TT deformation the degrees of freedom in subsystems are decreasing. This implies that the effect of the TT deformation can be regarded as the rescaling of the energy scale. We also study entanglement wedge cross section in cutoff AdS, and our result implies that for the entanglement of purification in the TT deformed CFTs phase transition could occur even for fixed subsystems.