Thermal States in Conformal QFT. I
Paolo Camassa, Roberto Longo, Yoh Tanimoto, Mih\'aly Weiner
TL;DR
This paper proves the uniqueness of the KMS state for completely rational conformal nets on the real line, showing it can be constructed geometrically and analyzing the thermal completion net.
Contribution
It establishes the uniqueness and geometric construction of KMS states for completely rational conformal nets, extending to two-dimensional cases.
Findings
Unique KMS state exists for completely rational nets.
The KMS state is constructed via a geometric procedure.
Similar uniqueness holds in two-dimensional conformal nets.
Abstract
We analyze the set of locally normal KMS states w.r.t. the translation group for a local conformal net A of von Neumann algebras on R. In this first part, we focus on completely rational net A. Our main result here states that, if A is completely rational, there exists exactly one locally normal KMS state \phi. Moreover, \phi is canonically constructed by a geometric procedure. A crucial r\^ole is played by the analysis of the "thermal completion net" associated with a locally normal KMS state. A similar uniqueness result holds for KMS states of two-dimensional local conformal nets w.r.t. the time-translation one-parameter group.
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