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Properties of Holographic Entanglement Entropy

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Holographic Entanglement Entropy

Part of the book series: Lecture Notes in Physics ((LNP,volume 931))

Abstract

The holographic RT and HRT prescriptions allow us to explore general properties of entanglement entropy in a class of QFTs. We will first examine the consistency of holographic entanglement entropy with expectations that follow from the basic definition as detailed in Sect. 2.4 We will also see that there are certain features that are peculiar to holographic systems, in part owing to the fact that we are working in the large c eff limit. We reiterate that the holographic entanglement entropy prescriptions are geared to capturing the leading semiclassical part of entanglement in terms of geometric data. Subleading corrections require ascertaining the bulk entanglement, as discussed in the previous section. All in all, this leads to some unexpected features, which at first sight seem unconventional, but are easily understood once one fully appreciates the implications of the limit c eff ≫ 1 being effectively a semiclassical regime of the QFT.

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Notes

  1. 1.

    We now set ℓ AdS = 1 to avoid cluttering up the notation. It can be reinstated through dimensional analysis.

  2. 2.

    With minor changes, we can make similar observations for the polar-cap regions of \(\mathbf{S}^{d-1} \times \mathbb{R}\).

  3. 3.

    This combination of entropies is also what appears in the computation of topological entanglement entropy for 2 + 1-dimensional theories, as originally described in [5].

  4. 4.

    The corresponding question for classical entropies has been successfully addressed in [127, 128], while that for quantum entanglement is as yet undetermined, though partial progress has been made in [129, 130].

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Authors and Affiliations

  1. Department of Physics, University of California, Center for Quantum Mathematics and Physics, Davis, CA, USA

    Mukund Rangamani

  2. Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kyoto, Japan

    Tadashi Takayanagi

  3. Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), University of Tokyo, Kashiwa, Chiba, Japan

    Tadashi Takayanagi

Authors
  1. Mukund Rangamani
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  2. Tadashi Takayanagi
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Rangamani, M., Takayanagi, T. (2017). Properties of Holographic Entanglement Entropy. In: Holographic Entanglement Entropy. Lecture Notes in Physics, vol 931. Springer, Cham. https://doi.org/10.1007/978-3-319-52573-0_6

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