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.