We consider KMS states on a local conformal net on the unit circle with respect to rotations. We prove that, if the conformal net is of type I, namely if it admits only type I DHR representations, then the extremal KMS states are the Gibbs states in an irreducible representation. Completely rational nets, the U(1)-current net, the Virasoro nets and their finite tensor products are shown to be of type I. In the completely rational case, we also give a direct proof that all factorial KMS states are Gibbs states.
Longo, R., Tanimoto, Y. (2018). Rotational KMS states and type I conformal nets. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 357(1), 249-266 [10.1007/s00220-017-2969-8].
Rotational KMS states and type I conformal nets
Longo, Roberto;Tanimoto, Yoh
2018-01-01
Abstract
We consider KMS states on a local conformal net on the unit circle with respect to rotations. We prove that, if the conformal net is of type I, namely if it admits only type I DHR representations, then the extremal KMS states are the Gibbs states in an irreducible representation. Completely rational nets, the U(1)-current net, the Virasoro nets and their finite tensor products are shown to be of type I. In the completely rational case, we also give a direct proof that all factorial KMS states are Gibbs states.File | Dimensione | Formato | |
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