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Toward Entanglement Entropy with UV-Cutoff in Conformal Nets

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Abstract

We consider the entanglement entropy for a spacetime region and its spacelike complement in the framework of algebraic quantum field theory. For a Möbius covariant local net (a chiral component of a two-dimensional conformal field theory) satisfying either a certain nuclearity property or the split property, we consider the von Neumann entropy for type I factors between local algebras and introduce an entropic quantity. Then we implement a cutoff on this quantity with respect to the conformal Hamiltonian and show that it remains finite as the distance of two intervals tends to zero. We compare our definition to others in the literature.

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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo, 153-8914, Japan

    Yul Otani

  2. Dipartimento di Matematica, Universitá di Roma Tor Vergata, Via della Ricerca Scientifica, 1, 00133, Rome, Italy

    Yoh Tanimoto

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  1. Yul Otani
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  2. Yoh Tanimoto
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Correspondence to Yoh Tanimoto.

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Communicated by Karl Henning Rehren.

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Otani, Y., Tanimoto, Y. Toward Entanglement Entropy with UV-Cutoff in Conformal Nets. Ann. Henri Poincaré 19, 1817–1842 (2018). https://doi.org/10.1007/s00023-018-0671-9

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  • DOI: https://doi.org/10.1007/s00023-018-0671-9

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