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Thermal States in Conformal QFT. I

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Abstract

We analyze the set of locally normal KMS states w.r.t. the translation group for a local conformal net \({{\mathcal A}}\) of von Neumann algebras on \({\mathbb R}\) . In this first part, we focus on the completely rational net \({{\mathcal A}}\) . Our main result here states that, if \({{\mathcal{A}}}\) is completely rational, there exists exactly one locally normal KMS state \({\varphi}\) . Moreover, \({\varphi}\) is canonically constructed by a geometric procedure. A crucial rôle is played by the analysis of the “thermal completion net” associated with a locally normal KMS state. A similar uniqueness result holds for KMS states of two-dimensional local conformal nets w.r.t. the time-translation one-parameter group.

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Authors and Affiliations

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

    Paolo Camassa, Roberto Longo, Yoh Tanimoto & Mihály Weiner

  2. Alfréd Rényi Institute of Mathematics, POB 127, 1364, Budapest, Hungary

    Mihály Weiner

Authors
  1. Paolo Camassa
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  2. Roberto Longo
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  3. Yoh Tanimoto
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  4. Mihály Weiner
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Corresponding author

Correspondence to Yoh Tanimoto.

Additional information

Communicated by Y. Kawahigashi

Research supported in part by the ERC Advanced Grant 227458 OACFT “Operator Algebras and Conformal Field Theory”, PRIN-MIUR, GNAMPA-INDAM and EU network “Noncommutative Geometry” MRTN-CT-2006-0031962.

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Camassa, P., Longo, R., Tanimoto, Y. et al. Thermal States in Conformal QFT. I. Commun. Math. Phys. 309, 703–735 (2012). https://doi.org/10.1007/s00220-011-1337-3

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  • DOI: https://doi.org/10.1007/s00220-011-1337-3

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