# Holographic Entanglement Entropy in Cutoff AdS

## TL;DR

This paper explores how holographic entanglement entropy behaves in cutoff AdS spaces, revealing effects of boost and $T ar{T}$ deformations on the entanglement structure and the $c$-function, consistent with the $c$-theorem.

## Contribution

It demonstrates that boost and $T ar{T}$ deformations in cutoff AdS can be understood as energy scale rescalings affecting entanglement entropy and the $c$-function, aligning with theoretical expectations.

## Key findings

- Boost affects entanglement entropy via length contraction.
- Deformations lead to a monotonic $c$-function flow from UV to IR.
- Holographic results match $T ar{T}$ deformed theories on a sphere.

## Abstract

We investigate the holographic entanglement entropy of deformed conformal field theories which are dual to a cutoff AdS space. The holographic entanglement entropy evaluated on a three-dimensional Poincare AdS space with a finite cutoff can be reinterpreted as that of the dual field theory deformed by either a boost or $T \bar{T}$ deformation. For the boost case, we show that, although it trivially acts on the underlying theory, it nontrivially affects the entanglement entropy due to the length contraction. For a three-dimensional AdS, we show that the effect of the boost transformation can be reinterpreted as the rescaling of the energy scale, similar to the $T \bar{T}$ deformation. Under the boost and $T \bar{T}$ deformation, the $c$-function of the entanglement entropy exactly shows the features expected by the Zamoldchikov's $c$-theorem. The deformed theory is always stationary at a UV fixed point and monotonically flows to another CFT in the IR fixed point. We also show that the holographic entanglement entropy in a Poincare cutoff AdS space can reproduce the exact same result of the $T \bar{T}$ deformed theory on a two-dimensional sphere.