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arXiv:2012.01895

Quantum entanglement measures from Hyperscaling violating geometries with finite radial cut off at general d, $θ$ from the emergent global symmetry

Chandrima Paul

Published Dec 3, 2020• 2 citations
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Abstract

The quantum entanglement measures for $T{\overline{T}}$ deformed field theory on boundary, deformation coefficient $μ$, with dual bulk geometry with finite radial cutoff $ρ_c$, for entangling region is single or disjoint intervals on the boundary, of length l is expected to give global description of these measures over the complete parameter-regime of $(l, μ)$ or on 2D $(l,ρ_c)$ plane, because it is solvable irrelevant deformation. Here, to find quantum-measures through RT prescription, from Hyperscaling violating bulk geometry with finite radial cut off, we found mathematically it is impossible, to obtain such global form, since the turning point $ρ_0 (l,ρ_c)$, neither in its exact or in any perturbative form, is solvable globally, can describe these quantum measures at most locally over some specific regime in 2D $(l,ρ_c)$ plane! However, to find such global form, we found, on application of RT formalism, a global symmetry structure, from the considered geometry emerges, over 2D parameter-space, irrespective of d, $θ$, which alongwith global b.c and other consistency conditions, fix $ρ_0(l,ρ_c)$ globally, exactly in $l >> ρ_c $ and $ρ_c >> l$ regime and as some interpolating expressions, very close to the exact one in other regime. Some of the quantum entanglement measures with this $ρ_0 (l,ρ_c)$, with our intuitively predicted behaviour for them in the deformed theory, derived and shown, behaving accordingly. The impact of this emergent symmetry on these quantum-measures is discussed, the possible space time origin of this symmetry is explored, although the later aspect is subjected to a proper and detailed study.

DOI
10.48550/arxiv.2012.01895

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Quantum entanglement measures from Hyperscaling violating geometries with finite radial cut off at general d, θθθ from the emergent global symmetry
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Abstract Recently, it was proposed that a TT‾ T\overline{T} TT T 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 ≥ I2 \frac{I}{2} 2I​ I 2 for all values of the cutoff.
Non-perturbative aspects of entanglement structures in TT‾T\overline{T }TT-deformed CFTs
A bstract Turning on the TT‾T\overline{T }TT -deformation in a two-dimensional CFT provides a unique window to study explicitly how non-local features arise in the UV as a result of the deformation. A sharp signature is the dynamical emergence of an effective length-scale ∝ μ\sqrt{\mu }μ​ that separates the local and non-local regimes of the deformed theory, effectively serving as a UV cut-off for computing observables in the local regime. In this paper, we study this phenomenon through the entanglement structures of the deformed theory. We focus on computing the Renyi entropies of single-interval sub-regions in the deformed vacuum states. We pay particular attention to the interplay between the bare entanglement cut-off inherited from the CFT computation and the effects from the TT‾T\overline{T }TT deformations. Applying the general replica trick to the string theory formulation of TT‾T\overline{T }TT -deformed CFTs, we derive an explicit representation of the deformed replica partition function as a weighted integral of the CFT results evaluated at a dynamical cut-off, which is integrated over. We computed in detail the kernel functions of the integral representation, and performed the saddle-point analysis in the semi-classical limit of small μ . We found that in addition to the perturbative saddle-point which identifies the dynamical cut-off with the bare entanglement cut-off, there exists another non-perturbative saddle-point that identifies the dynamical cut-off with the TT‾T\overline{T }TT length-scale ∝ μ\sqrt{\mu }μ​ , but whose contribution is exponentially small. We discuss how these non-perturbative effects can shed lights on the mechanism through which the TT‾T\overline{T }TT length-scale may eventually replace the bare counter-part and become the effective entanglement cut-off.
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Quantum gravity in a finite region of spacetime is conjectured to be dual to a conformal field theory (CFT) deformed by the irrelevant operator TT[over ¯]. We test this conjecture with entanglement entropy, which is sensitive to ultraviolet physics on the boundary, while also probing the bulk geometry. We find that the entanglement entropy for an entangling surface consisting of two antipodal points on a sphere is finite and precisely matches the Ryu-Takayanagi formula applied to a finite region consistent with the conjecture of McGough et al. We also consider a one-parameter family of conical entropies, which are finite and verify a conjecture due to Dong. Since ultraviolet divergences are local, we conclude that the TT[over ¯] deformation acts as an ultraviolet cutoff on the entanglement entropy. Our results support the conjecture that the TT[over ¯]-deformed CFT is the holographic dual of a finite region of spacetime.