Communications in Mathematical Physics

, Volume 315, Issue 3, pp 771–802

Thermal States in Conformal QFT. II

  • Paolo Camassa
  • Roberto Longo
  • Yoh Tanimoto
  • Mihály Weiner
Open Access
Article

Abstract

We continue the analysis of 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 the first part we have proved the uniqueness of the KMS state on every completely rational net. In this second part, we exhibit several (non-rational) conformal nets which admit continuously many primary KMS states. We give a complete classification of the KMS states on the U(1)-current net and on the Virasoro net Vir1 with the central charge c = 1, whilst for the Virasoro net Vir c with c > 1 we exhibit a (possibly incomplete) list of continuously many primary KMS states. To this end, we provide a variation of the Araki-Haag-Kastler-Takesaki theorem within the locally normal system framework: if there is an inclusion of split nets \({\mathcal{A}\subset \mathcal{B}}\) and \({\mathcal{A}}\) is the fixed point of \({\mathcal{B}}\) w.r.t. a compact gauge group, then any locally normal, primary KMS state on \({\mathcal{A}}\) extends to a locally normal, primary state on \({\mathcal{B}}\) , KMS w.r.t. a perturbed translation. Concerning the non-local case, we show that the free Fermi model admits a unique KMS state.

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Copyright information

© The Author(s) 2012

Authors and Affiliations

  • Paolo Camassa
    • 1
  • Roberto Longo
    • 1
  • Yoh Tanimoto
    • 1
  • Mihály Weiner
    • 1
    • 2
  1. 1.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItaly
  2. 2.Department of AnalysesBudapest University of Technology and EconomicsBudapestHungary

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