Timelike entanglement entropy and $T\bar{T}$ deformation

Jiang, Xin; Wang, Peng; Wu, Houwen; Yang, Haitang

doi:10.48550/arxiv.2302.13872

Cited by 2 publications

(3 citation statements)

References 13 publications

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“…The real part corresponds to the spacelike interval in the sphere instanton, while the imaginary part is for a timelike interval in dS space. See [144][145][146][147][148][149][150][151] for recent discussion about its analytical continuation in AdS/CFT context to a different notion, named timelike entanglement entropy. Our wedge holographic proposal might provide a new test ground for such types of generalized notions of holographic entanglement entropy in dS space.…”

Section: Discussion and Outlookmentioning

confidence: 99%

“…The key difference from the standard wedge holographic settings is that, in the case of dS branes, the defects represent Euclidean CFTs and are timelike separated. Thus, the notion of entanglement that we need would be a version of "pseudo entropy" recently introduced in [142][143][144][145][146] or "timelike entanglement entropy" [144][145][146][147][148][149][150][151]. We argue that, from the braneworld perspective, the holographic dual of this quantity would correspond to the area of an extremal surface connecting subregions in the two defects.…”

Section: Entanglement Entropy Between the Codimension-2 Defectsmentioning

confidence: 99%

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Entangled universes in dS wedge holography

Aguilar-Gutierrez,

Patra,

Pedraza

2023

J. High Energ. Phys.

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We develop a new setting in the framework of braneworld holography to describe a pair of coupled and entangled uniformly accelerated universes. The model consists of two branes embedded into AdS space capping off the UV and IR regions, giving rise to a notion of dS wedge holography. Specializing in a three-dimensional bulk, we show that dS JT gravity can emerge as an effective braneworld theory, provided that fluctuations transverse to the branes are included. We study the holographic entanglement entropy between the branes as well as the holographic complexity within the ‘complexity=anything’ proposal. We reproduce a Page curve with respect to an observer collecting radiation on the UV brane, as long as we take the limit where gravity decouples in that universe, thus acting as a non-gravitating bath. The Page curve emerges due to momentum-space (UV/IR) entanglement and can be understood as analogous to the ‘confinement-deconfinement’ transition in theories with a mass gap. Moreover, the analysis of complexity shows that the hyperfast growth phenomenon is displayed within a set of proposals, while late-time linear growth can be recovered for a different set. Our framework thus provides new test grounds for understanding quantum information concepts in dS space and dS holography.

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Section: Discussion and Outlookmentioning

confidence: 99%

Section: Entanglement Entropy Between the Codimension-2 Defectsmentioning

confidence: 99%

Entangled universes in dS wedge holography

Aguilar-Gutierrez,

Patra,

Pedraza

2023

J. High Energ. Phys.

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“…Furthermore, the anisotropy between the temporal and spatial directions in LFTs makes it interesting to investigate the behavior of entanglement entropy in the time direction. In this context, we compute the time-like entanglement entropy using the holographic prescription of [45,46] (See [47][48][49][50][51][52][53][54][55][56] for recent developments). The holographic result is z-dependent and suggests that there exists a fundamental definition of time-like entanglement entropy other than employing analytic continuation.…”

Section: Jhep05(2024)284mentioning

confidence: 99%

Massless Lifshitz field theory for arbitrary z

Basak,

Chakraborty,

Chu

et al. 2024

J. High Energ. Phys.

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By using the notion of fractional derivatives, we introduce a class of massless Lifshitz scalar field theory in (1+1)-dimension with an arbitrary anisotropy index z. The Lifshitz scale invariant ground state of the theory is constructed explicitly and takes the form of Rokhsar-Kivelson (RK). We show that there is a continuous family of ground states with degeneracy parameterized by the choice of solution to the equation of motion of an auxiliary classical system. The quantum mechanical path integral establishes a 2d/1d correspondence with the equal time correlation functions of the Lifshitz scalar field theory. We study the entanglement properties of the Lifshitz theory for arbitrary z using the path integral representation. The entanglement measures are expressed in terms of certain cross ratio functions we specify, and satisfy the c-function monotonicity theorems. We also consider the holographic description of the Lifshitz theory. In order to match with the field theory result for the entanglement entropy, we propose a z-dependent radius scale for the Lifshitz background. This relation is consistent with the z-dependent scaling symmetry respected by the Lifshitz vacuum. Furthermore, the time-like entanglement entropy is determined using holography. Our result suggests that there should exist a fundamental definition of time-like entanglement other than employing analytic continuation as performed in relativistic field theory.

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Timelike entanglement entropy and $T\bar{T}$ deformation

Cited by 2 publications

References 13 publications

Entangled universes in dS wedge holography

Entangled universes in dS wedge holography

Massless Lifshitz field theory for arbitrary z

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