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VOL. 80 | 2019 KMS states on conformal QFT
Yoh Tanimoto

Editor(s) Masaki Izumi, Yasuyuki Kawahigashi, Motoko Kotani, Hiroki Matui, Narutaka Ozawa

Abstract

Some recent results on KMS states on chiral components of two-dimensional conformal quantum field theories are reviewed. A chiral component is realized as a conformal net of von Neumann algebras on a circle, and there are two natural choices of dynamics: rotations and translations.

For rotations, the natural choice of the algebra is the universal $C^*$-algebra. We classify KMS states on a large class of conformal nets by their superselection sectors. They can be decomposed into Gibbs states with respect to the conformal Hamiltonian.

For translations, one can consider the quasilocal $C^*$-algebra and we construct a distinguished geometric KMS state on it, which results from diffeomorphism covariance. We prove that this geometric KMS state is the only KMS state on a completely rational net. For some non-rational nets, we present various different KMS states.

Information

Published: 1 January 2019
First available in Project Euclid: 21 August 2019

zbMATH: 07116430
MathSciNet: MR3966591

Digital Object Identifier: 10.2969/aspm/08010211

Subjects:
Primary: 46L60, 81T05, 81T40

Rights: Copyright © 2019 Mathematical Society of Japan

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