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High Energy Physics - Theory

arXiv:2111.03886 (hep-th)
[Submitted on 6 Nov 2021 (v1), last revised 26 Mar 2022 (this version, v3)]

Title:Defining entanglement without tensor factoring: a Euclidean hourglass prescription

Authors:Takanori Anegawa, Norihiro Iizuka, Daniel Kabat
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Abstract:We consider entanglement across a planar boundary in flat space. Entanglement entropy is usually thought of as the von Neumann entropy of a reduced density matrix, but it can also be thought of as half the von Neumann entropy of a product of reduced density matrices on the left and right. The latter form allows a natural regulator in which two cones are smoothed into a Euclidean hourglass geometry. Since there is no need to tensor-factor the Hilbert space, the regulated entropy is manifestly gauge-invariant and has a manifest state-counting interpretation. We explore this prescription for scalar fields, where the entropy is insensitive to a non-minimal coupling, and for Maxwell fields, which have the same entropy as $d-2$ scalars.
Comments: 25 pages. v2: references added. v3: version to appear in PRD
Subjects: High Energy Physics - Theory (hep-th)
Cite as: arXiv:2111.03886 [hep-th]
  (or arXiv:2111.03886v3 [hep-th] for this version)
  https://doi.org/10.48550/arXiv.2111.03886
Related DOI: https://doi.org/10.1103/PhysRevD.105.085003

Submission history

From: Daniel Kabat [view email]
[v1] Sat, 6 Nov 2021 13:44:49 UTC (89 KB)
[v2] Sat, 20 Nov 2021 20:47:06 UTC (89 KB)
[v3] Sat, 26 Mar 2022 20:52:06 UTC (90 KB)
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