Moduli spaces of Dirac operators for finite spectral triples

TL;DR

This paper generalizes the structure theory of finite real spectral triples to include arbitrary KO-dimension and non-orientability, defining and analyzing their moduli spaces of Dirac operators, with applications to the noncommutative Standard Model.

Contribution

It extends existing theory to more general spectral triples and studies their moduli spaces, connecting to the noncommutative Standard Model.

Findings

Generalized the structure theory of finite real spectral triples.

Defined and studied moduli spaces of Dirac operators for these triples.

Applied the theory to noncommutative geometry models of the Standard Model.

Abstract

The structure theory of finite real spectral triples developed by Krajewski and by Paschke and Sitarz is generalised to allow for arbitrary KO-dimension and the failure of orientability and Poincare duality, and moduli spaces of Dirac operators for such spectral triples are defined and studied. This theory is then applied to recent work by Chamseddine and Connes towards deriving the finite spectral triple of the noncommutative-geometric Standard Model.