# Thermal States in Conformal QFT. II

September 09, 2011

We continue the analysis of the set of locally normal KMS states w.r.t. the
translation group for a local conformal net A of von Neumann algebras on the
real line. In the first part we have proved the uniqueness of 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 Vir_1 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 A in B and A is the fixed point of B
w.r.t. a compact gauge group, then any locally normal, primary KMS state on A
extends to a locally normal, primary state on 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.

open access link
Commun. Math. Phys. Vol. 315, No. 3 (2012), 771-802

@article{Camassa:2011wk,
author = "Camassa, Paolo and Longo, Roberto and Tanimoto, Yoh and
Weiner, Mihaly",
title = "{Thermal States in Conformal QFT. II}",
journal = "Commun. Math. Phys.",
volume = "315",
year = "2012",
pages = "771-802",
doi = "10.1007/s00220-012-1514-z",
eprint = "1109.2064",
archivePrefix = "arXiv",
primaryClass = "math-ph",
SLACcitation = "%%CITATION = ARXIV:1109.2064;%%"
}

Keywords:

*none*