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arXiv:1904.06930

Comments on holographic entanglements in cutoff AdS

Ota, Toshihiro

Published Apr 15, 2019• 14 citations
arXivHTMLPDF

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.

DOI
10.48550/arxiv.1904.06930

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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.
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.
In this work, we study the holographic entanglement entropy in AdS3 gravity with the certain mixed boundary condition, which turns out to correspond to TT¯-deformed 2D CFTs. By employing the Chern-Simons formalism and Wilson line technique, the holographic entanglement entropy in TT¯-deformed BTZ black hole is obtained. We also get the same formula by calculating the RT surface. The holographic entanglement entropy agrees with the perturbation result derived from both TT¯-deformed CFTs and cutoff AdS3. Moreover, our result shows that the deformed entanglement entropy for large deformation parameter behaves like the entanglement entropy of CFT at zero temperature. We also consider the entanglement entropy of two intervals and study the effect of TT¯ deformation on phase transition.
A bstract Recently it was proposed that, the AdS/BCFT correspondence can be simulated by a holographic Weyl transformed CFT 2 , where the cut-off brane plays the role of the Karch-Randall (KR) brane [1]. In this paper, we focus on the Weyl transformation that optimizes the path integral computation of the reduced density matrix for a single interval in a holographic CFT 2 . When we take the limit that one of the endpoint of the interval goes to infinity (a half line), such a holographic Weyl transformed CFT 2 matches the AdS/BCFT configuration for a BCFT with one boundary. Without taking the limit, the induced cutoff brane becomes a circle passing through the two endpoints of the interval. We assume that the cutoff brane also plays the same role as the KR brane in AdS/BCFT, hence the path-integral-optimized purification for the interval is in the island phase. This explains the appearance of negative mutual information observed in [2]. We check that, the entanglement entropy and the balanced partial entanglement entropy (BPE) calculated via the island formulas, exactly match with the RT formula and the entanglement wedge cross-section (EWCS), which are allowed to anchor on the cutoff brane.
A bstract We compute holographic entanglement entropy (EE) and the renormalized EE in AdS solitons with gauge potential for various dimensions. The renormalized EE is a cutoff-independent universal component of EE. Via Kaluza-Klein compactification of S 1 and considering the low-energy regime, we deduce the ( d − 1)-dimensional renormalized EE from the odd-dimensional counterpart. This corresponds to the shrinking circle of AdS solitons, probed at large l . The minimal surface transitions from disk to cylinder dominance as l increases. The quantum phase transition occurs at a critical subregion size, with renormalized EE showing non-monotonic behavior around this size. Across dimensions, massive modes decouple at lower energy, while degrees of freedom with Wilson lines contribute at smaller energy scales.
We study the entanglement entropy (EE) and the R\'enyi entropy (RE) of multiple intervals in two-dimensional TT‾T\overline{T}TT- deformed conformal field theory (CFT) at a finite temperature by field theoretic and holographic methods. First, by the replica method with the twist operators, we construct the general formula of the RE and EE up to the first order of a deformation parameter. By using our general formula, we show that the EE of multiple intervals for a holographic CFT is just a summation of the single interval case even with the small deformation. This is a nontrivial consequence from the field theory perspective, though it may be expected by the Ryu-Takayanagi formula in holography. However, the deformed RE of the two intervals is a summation of the single interval case only if the separations between the intervals are big enough. It can be understood by the tension of the cosmic branes dual to the RE. We also study the holographic EE for single and two intervals with an arbitrary cutoff radius (dual to the TT‾T\overline{T}TT deformation) at any temperature. We confirm our holographic results agree with the field theory results with a small deformation and high temperature limit, as expected. For two intervals, there are two configurations for EE: disconnected (sss-channel) and connected (ttt-channel) ones. We investigate the phase transition between them as we change parameters: as the deformation or temperature increases the phase transition is suppressed and the disconnected phase is more favored.
We study mixed state entanglement measures in a higher dimensional T T ¯ deformed field theory at finite temperature. The holographic dual is described by AdS d + 1 black brane geometry with a finite cutoff. We compute the entanglement wedge cross section (EWCS), proposed to be dual to entanglement of purification and holographic entanglement negativity (HEN) for striplike subsystems. The behavior of EWCS and HEN is studied across different regimes of temperature and deformation parameter. It is observed that the deformation and temperature exhibit similar effects on these two entanglement measures. Increasing the deformation leads to a decrease in the entanglement between the subsystems.