## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- 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

### KMS states on conformal QFT

#### 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

**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