Advanced Studies in Pure Mathematics

KMS states on conformal QFT

Yoh Tanimoto

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
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

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

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1566404317

Digital Object Identifier
doi:10.2969/aspm/08010211

Mathematical Reviews number (MathSciNet)
MR3966591

Zentralblatt MATH identifier
07116430

Subjects
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]

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

Citation

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. https://projecteuclid.org/euclid.aspm/1566404317


Export citation