Thursday, March 1, 2012

1101.2865 (Paolo Camassa et al.)

Thermal States in Conformal QFT. I    [PDF]

Paolo Camassa, Roberto Longo, Yoh Tanimoto, Mihály Weiner
We analyze the set of locally normal KMS states w.r.t. the translation group for a local conformal net A of von Neumann algebras on R. In this first part, we focus on completely rational net A. Our main result here states that, if A is completely rational, there exists exactly one locally normal KMS state \phi. Moreover, \phi is canonically constructed by a geometric procedure. A crucial r\^ole 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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