Differential $KO$-theory via gradations and mass terms

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.