Thermal States in Conformal QFT. II

We continue the analysis of the set of locally normal KMS states w.r.t. the translation group for a local conformal net A of von Neumann algebras on the real line. In the first part we have proved the uniqueness of KMS state on every completely rational net. In this second part, we exhibit several (non-rational) conformal nets which admit continuously many primary KMS states. We give a complete classification of the KMS states on the U(1)-current net and on the Virasoro net Vir_1 with the central charge c=1, whilst for the Virasoro net Vir_c with c>1 we exhibit a (possibly incomplete) list of continuously many primary KMS states. To this end, we provide a variation of the Araki-Haag-Kastler-Takesaki theorem within the locally normal system framework: if there is an inclusion of split nets A in B and A is the fixed point of B w.r.t. a compact gauge group, then any locally normal, primary KMS state on A extends to a locally normal, primary state on B, KMS w.r.t. a perturbed translation. Concerning the non-local case, we show that the free Fermi model admits a unique KMS state.Comment: 36 pages, no figure. Dedicated to Rudolf Haag on the occasion of his 90th birthday. The final version is available under Open Access. This paper contains corrections to the Araki-Haag-Kaster-Takesaki theorem (and to a proof of the same theorem in the book by Bratteli-Robinson). v3: a reference correcte

El teorema del punto fijo de Zermelo en los conjuntos parcialmente ordenados y los principios transfinitos de existencia

Existen varios principios transfinitos de existencia equivalentes entre sí. Se sabe que todos ellos son independientes de los otros principios (axiomas) de la teoría de conjuntos y por lo tanto no pueden “demostrarse" sino únicamente aceptarlos o rechazarlos como axioma

El teorema del punto fijo de zermelo en los conjuntos parcialmente ordenados y los principios transfinitos de existencia.

Existen varios principios transfinitos de existencia equivalentes entre sí. Se sabe que todos ellos son independientes de los otros principios (axiomas) de la teoría de conjuntos y por lo tanto no pueden “demostrarse" sino únicamente aceptarlos o rechazarlos como axiomas