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Rotational KMS States and Type I Conformal Nets

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Abstract

We consider KMS states on a local conformal net on S 1 with respect to rotations. We prove that, if the conformal net is of type I, namely if it admits only type I DHR representations, then the extremal KMS states are the Gibbs states in an irreducible representation. Completely rational nets, the U(1)-current net, the Virasoro nets and their finite tensor products are shown to be of type I. In the completely rational case, we also give a direct proof that all factorial KMS states are Gibbs states.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Rome, Italy

    Roberto Longo & Yoh Tanimoto

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  1. Roberto Longo
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  2. Yoh Tanimoto
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Correspondence to Roberto Longo.

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Communicated by D. Buchholz, K. Fredenhagen, Y. Kawahigashi

R. Longo: Supported in part by the ERC Advanced Grant 669240 QUEST “Quantum Algebraic Structures and Models”, PRIN-MIUR, GNAMPA-INdAM and Alexander von Humboldt Foundation.

Y. Tanimoto: Supported by the JSPS fellowship for research abroad.

2017 by the authors. This article may be reproduced in its entirety for non-commercial purposes.

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Longo, R., Tanimoto, Y. Rotational KMS States and Type I Conformal Nets. Commun. Math. Phys. 357, 249–266 (2018). https://doi.org/10.1007/s00220-017-2969-8

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