We continue the analysis of the set of locally normal KMS states w.r.t. the translation group for a local conformal net of von Neumann algebras on . In the first part we have proved the uniqueness of the 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 and is the fixed point of w.r.t. a compact gauge group, then any locally normal, primary KMS state on extends to a locally normal, primary state on , KMS w.r.t. a perturbed translation. Concerning the non-local case, we show that the free Fermi model admits a unique KMS state.

Camassa, P., Longo, R., Tanimoto, Y., Weiner, M. (2012). Thermal States in Conformal QFT. II. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 315(3), 771-802 [10.1007/s00220-012-1514-z].

Thermal States in Conformal QFT. II

CAMASSA, PAOLO;LONGO, ROBERTO;Tanimoto, Y;
2012-01-01

Abstract

We continue the analysis of the set of locally normal KMS states w.r.t. the translation group for a local conformal net of von Neumann algebras on . In the first part we have proved the uniqueness of the 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 and is the fixed point of w.r.t. a compact gauge group, then any locally normal, primary KMS state on extends to a locally normal, primary state on , KMS w.r.t. a perturbed translation. Concerning the non-local case, we show that the free Fermi model admits a unique KMS state.
2012
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Operator Algebras, Quantum Field Theory, Mathematical Physics
Camassa, P., Longo, R., Tanimoto, Y., Weiner, M. (2012). Thermal States in Conformal QFT. II. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 315(3), 771-802 [10.1007/s00220-012-1514-z].
Camassa, P; Longo, R; Tanimoto, Y; Weiner, M
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/89977
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