Local-entire cyclic cocycles for graded quantum field nets

TL;DR

This paper introduces local-entire cyclic cocycles derived from super-KMS functionals on graded quantum field nets, enabling the assignment of noncommutative geometric invariants to these systems.

Contribution

It demonstrates that super-KMS functionals induce local-entire cyclic cocycles, extending noncommutative geometric tools to graded quantum dynamical systems.

Findings

Super-KMS functionals produce local-entire cyclic cocycles.

These cocycles are homotopy-invariant under certain perturbations.

Application to graded quantum field nets yields new invariants.

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.