Advanced Studies in Pure Mathematics

KMS states on conformal QFT

Yoh Tanimoto

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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.

Article information

Operator Algebras and Mathematical Physics, M. Izumi, Y. Kawahigashi, M. Kotani, H. Matui and N. Ozawa, eds. (Tokyo: Mathematical Society of Japan, 2019), 211-218

Received: 31 December 2017
First available in Project Euclid: 21 August 2019

Permanent link to this document euclid.aspm/1566404317

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 81T40: Two-dimensional field theories, conformal field theories, etc. 81T05: Axiomatic quantum field theory; operator algebras 46L60: Applications of selfadjoint operator algebras to physics [See also 46N50, 46N55, 47L90, 81T05, 82B10, 82C10]

operator algebras conformal field theory algebraic quantum field theory modular theory thermal states KMS states


Tanimoto, Yoh. KMS states on conformal QFT. Operator Algebras and Mathematical Physics, 211--218, Mathematical Society of Japan, Tokyo, Japan, 2019. doi:10.2969/aspm/08010211.

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