On Super-KMS Functionals for Graded-Local Conformal Nets

Details On Super-KMS Functionals for Graded-Local Conformal Nets On Super-KMS Functionals for Graded-Local Conformal Nets

2012-04-23

arxiv.org/abs/1204.5078v1

Mathematics

Operator Algebras

37 pages

Scientific paper

Motivated by a few preceding works, we introduce super-KMS functionals for graded-local conformal nets with superderivations, roughly speaking as a certain supersymmetric modification of classical KMS states on local conformal nets. Although we are able to make several surprising statements concerning their general structure, most properties will be studied in the setting of individual models. In particular, we provide a constructive existence and partial uniqueness proof of super-KMS functionals for the supersymmetric free field in d dimensions, for its rational extensions, and for the super-Virasoro net. As a general tool we develop a quasi-equivalence criterion for certain functionals on the CAR algebra in the sense of Araki. Moreover, we show that super-KMS functionals - as one of their main applications - give rise to generalized perturbation-invariant entire cyclic (JLO) cocycles and thus to a connection with noncommutative geometry.

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