Thermal States in Conformal QFT. I

Paolo Camassa, Roberto Longo, Yoh Tanimoto, Mihaly Weiner
January 14, 2011
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.
open access link Commun. Math. Phys. Vol. 309, No. 3 (2012), 703-735
@article{Camassa:2011te, author = "Camassa, Paolo and Longo, Roberto and Tanimoto, Yoh and Weiner, Mihaly", title = "{Thermal States in Conformal QFT. I}", journal = "Commun. Math. Phys.", volume = "309", year = "2012", pages = "5", doi = "10.1007/s00220-011-1337-3", eprint = "1101.2865", archivePrefix = "arXiv", primaryClass = "math-ph", SLACcitation = "%%CITATION = ARXIV:1101.2865;%%" }