Thermal States in Conformal QFT. I

Details Thermal States in Conformal QFT. I Thermal States in Conformal QFT. I

2011-01-14

arxiv.org/abs/1101.2865v2

Commun. Math. Phys. Vol. 309, No. 3 (2012), 703-735

Physics

Mathematical Physics

38 pages

Scientific paper

10.1007/s00220-011-1337-3

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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