Effects of non-conformal boundary on entanglement entropy
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Springer
Received: April Revised: September Accepted: September Published: October
21, 11, 16, 23,
2020 2020 2020 2020
Andrew Loveridge Department of Physics, University of Texas at Austin, 2515 Speedway, Austin, Texas 78712, U.S.A.
E-mail: [email protected] Abstract: Spacetime boundaries with canonical Neuman or Dirichlet conditions preserve conformal invarience, but “mixed” boundary conditions which interpolate linearly between them can break conformal symmetry and generate interesting Renormalization Group flows even when a theory is free, providing soluble models with nontrivial scale dependence. We compute the (Rindler) entanglement entropy for a free scalar field with mixed boundary conditions in half Minkowski space and in Anti-de Sitter space. In the latter case we also compute an additional geometric contribution, which according to a recent proposal then collectively give the 1/N corrections to the entanglement entropy of the conformal field theory dual. We obtain some perturbatively exact results in both cases which illustrate monotonic interpolation between ultraviolet and infrared fixed points. This is consistent with recent work on the irreversibility of renormalization group, allowing some assessment of the aforementioned proposal for holographic entanglement entropy and illustrating the generalization of the g-theorem for boundary conformal field theory. Keywords: 1/N Expansion, AdS-CFT Correspondence, Boundary Quantum Field Theory, Renormalization Group ArXiv ePrint: 2004.07870
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)151
JHEP10(2020)151
Effects of non-conformal boundary on entanglement entropy
Contents 1 Introduction
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2 Preliminaries and methods
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3 Half Minkowski space
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5 Discussion and conclusions
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A Details of half Minkowski space calculations
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B Details of Anti-de Sitter space calculations B.1 Entropic contribution B.2 Geometric contribution
21 21 22
1
Introduction
The entropy of entanglement, famously elucidated in early debates on the nature of quantum mechanics,1 has emerged more recently as a powerful unifying tool in quantum field theory. It can act as an order parameter for phase transitions [1–4], has provocative links with the black hole entropy formula [5, 6], has assisted in generalizing the c-theorem to higher dimensions [7, 9], and appears to play a role in the holographic emergence of spacetime geometry [10–12] in the AdS/CFT correspondence [13–15]. Despite the utility of the quantity, it remains notoriously difficult to compute. Most examples involve only free fields [16] or exploit conformal symmetry [17, 18]. This is unfortunate since some highly interesting applications involve the renormalization group flow of the entanglement entropy, as alluded to above. For a spacetime without boundary the leading contribution to the entanglment entropy of a quantum field theory is the area law [19]. That is, if one considers the entropy as a function of the scale of the region, the dominant co
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