KMS states on conformal QFT. (English) Zbl 1425.81089
Izumi, Masaki (ed.) et al., Operator algebras and mathematical physics. Proceedings of the 9th international conference on operator algebras and mathematical physics, Tohoku University, Sendai, Japan, August 1–12, 2016. Tokyo: Mathematical Society of Japan. Adv. Stud. Pure Math. 80, 211-218 (2019).
Summary: 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.
For the entire collection see [Zbl 1420.46001].
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.
For the entire collection see [Zbl 1420.46001].
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81T05 | Axiomatic quantum field theory; operator algebras |
| 46L60 | Applications of selfadjoint operator algebras to physics |
| 46L30 | States of selfadjoint operator algebras |
| 82B30 | Statistical thermodynamics |
| 81T27 | Continuum limits in quantum field theory |
| 81T28 | Thermal quantum field theory |
| 46L05 | General theory of \(C^*\)-algebras |
