Rotational KMS states and type I conformal nets

Roberto Longo, Yoh Tanimoto
August 31, 2016
We consider KMS states on a local conformal net on the unit circle with respect to rotations. We prove that, if the conformal net is of type I, namely if it admits only type I DHR representations, then the extremal KMS states are the Gibbs states in an irreducible representation. Completely rational nets, the U(1)-current net, the Virasoro nets and their finite tensor products are shown to be of type I. In the completely rational case, we also give a direct proof that all factorial KMS states are Gibbs states.
open access link doi:10.1007/s00220-017-2969-8
@article{Longo:2016pci, author = "Longo, Roberto and Tanimoto, Yoh", title = "{Rotational KMS states and type I conformal nets}", journal = "Commun. Math. Phys.", volume = "357", year = "2018", number = "1", pages = "249-266", doi = "10.1007/s00220-017-2969-8", eprint = "1608.08903", archivePrefix = "arXiv", primaryClass = "math-ph", SLACcitation = "%%CITATION = ARXIV:1608.08903;%%" }