Abstract
In a recent paper we studied general properties of super-KMS functionals on graded quantum dynamical systems coming from graded translation-covariant quantum field nets over \({\mathbb{R}}\), and we carried out a detailed analysis of these objects on certain models of superconformal nets. In the present article, we show that these locally bounded functionals give rise to local-entire cyclic cocycles (generalized JLO cocycles) which are homotopy-invariant for a suitable class of perturbations of the dynamical system. Thus we can associate meaningful noncommutative geometric invariants to those graded quantum dynamical systems.
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Formerly supported as Marie-Curie Fellow of the Istituto Nazionale di Alta Matematica, Roma, and by the ERC Advanced Grant 227458 “Operator Algebras and Conformal Field Theory”.
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Hillier, R. Local-Entire Cyclic Cocycles for Graded Quantum Field Nets. Lett Math Phys 104, 271–298 (2014). https://doi.org/10.1007/s11005-013-0662-1
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DOI: https://doi.org/10.1007/s11005-013-0662-1