Noncommutative Geometric Gauge Theory from Superconnections

Abstract

Noncommutative geometric gauge theory is reconstructed based on the superconnection concept. The bosonic action of the Connes-Lott model including the symmetry breaking Higgs sector is obtained by using a new generalized derivative, which consists of the usual 1-form exterior derivative plus an extra element called the matrix derivative, for the curvatures. We first derive the matrix derivative based on superconnections and then show how the matrix derivative can give rise to spontaneous symmetry breaking. We comment on the correspondence between the generalized derivative and the generalized Dirac operator of the Connes-Lott model.