Abstract
Recently, it was proposed that a Toverline{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 EW ≥ frac{I}{2} for all values of the cutoff.
Highlights
The aim of this paper is to explore the effects of a finite radial cutoff in the bulk spacetime on some of the quantum entanglement measures such as Holographic Entanglement Entropy (HEE), Mutual Information (HMI), and Entanglement Wedge Cross Section (EWCS) in these geometries when the entangling regions are in the shape of strips
One might conclude that the quantum correlations among the degrees of freedom decrease by increasing the cutoff
We considered a Hyperscaling Violating (HV) geometry at zero temperature and finite radial cutoff, which one might expect to be dual to a T T deformed quantum field theory (QFT) in which the Lorentz and scaling symmetries are broken
Summary
We first review some properties of T T -deformed CFTs in d+1 dimensions. It should be pointed out that when the boundary manifold is curved or there are matter fields in the bulk spacetime, one should add more terms on both sides of the above equation [4, 7, 11, 12] Another amazing property of T T -deformed CFTs is the factorization property [1, 4, 7] of the deformation operator. Which has a prominent role in obtaining exact results in the deformed CFT, such as in the calculation of energy levels This property was proved in two dimensions [1] and expected to be valid in higher dimensions in the large N limit [7, 11, 25] (see [4])
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