Differential $KO$-theory via gradations and mass terms

TL;DR

This paper develops models of differential KO-theory and twisted differential KO-theory using gradations on Clifford modules, extending superconnection formalism and relating to fermionic mass terms in physics.

Contribution

It introduces new models of differential KO-theory based on gradations on Clifford modules and generalizes superconnection formalism for these models.

Findings

Constructed models of differential KO-theory and twisted variants

Extended superconnection formalism to Clifford modules

Linked models to fermionic mass terms in physics

Abstract

We construct models of the differential $KO$-theory and the twisted differential $KO$-theory, by refining Karoubi's $KO$-theory [Kar78] in terms of gradations on Clifford modules. In order for this, we set up the generalized Clifford superconnection formalism which generalizes the Quillen's superconnection formalism [Qui85]. One of our models can be regarded as classifying "fermionic mass terms" in physics.