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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


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.


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

zbMATH: 07116430
MathSciNet: MR3966591

Digital Object Identifier: 10.2969/aspm/08010211

Primary: 46L60, 81T05, 81T40

Rights: Copyright © 2019 Mathematical Society of Japan


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