On Super-KMS Functionals for Graded-Local Conformal Nets
Robin Hillier
April 24, 2012
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.
Keywords:
chiral conformal field theory, entire cyclic cohomology, KMS condition, supersymmetry