Local-entire cyclic cocycles for graded quantum field nets

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 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. Thus we can associate meaningful noncommutative geometric invariants to those graded quantum dynamical systems.

21 pages. Built on a section that has been removed from the old preprint 1204.5078v2 when passing to 1204.5078v3. arXiv admin note: substantial text overlap with arXiv:1204.5078v2. v2: Citations and outlook remark added, few typographical and stylistic corrections. v3: minor correction, final published version