Aspects of Hyperscaling Violating Geometries at Finite Cutoff

TL;DR

This paper investigates the effects of finite radial cutoff on hyperscaling violating geometries, analyzing holographic entanglement measures and revealing how cutoff influences phase transitions and geometric bounds.

Contribution

It provides new insights into how finite cutoff modifies holographic entanglement entropy, mutual information, and entanglement wedge cross section in hyperscaling violating geometries.

Findings

Mutual information decreases with increasing cutoff.

Entanglement wedge cross section remains finite and satisfies bounds at all cutoffs.

Phase transition points shift with cutoff, affecting entanglement properties.

Abstract

Recently, it was proposed that a $T\overline{T}$ deformed CFT is dual to a gravity theory in an asymptotically AdS spacetime at finite radial cutoff. Motivated by this proposal, we explore some aspects of Hyperscaling Violating geometries at finite cutoff and zero temperature. We study holographic entanglement entropy, mutual information (HMI) and entanglement wedge cross section (EWCS) for entangling regions in the shape of strips. It is observed that the HMI shows interesting features in comparison to the very small cutoff case: It is a decreasing function of the cutoff. It is finite when the distance between the two entangling regions goes to zero. The location of its phase transition also depends on the cutoff, and decreases by increasing the cutoff. On the other hand, the EWCS is a decreasing function of the cutoff. It does not show a discontinuous phase transition when the HMI undergoes a first-order phase transition. However, its concavity changes. Moreover, it is finite when the distance between the two strips goes to zero. Furthermore, it satisfies the bound $ E_W \geq \frac{I}{2}$ for all values of the cutoff.