Noncommutative Geometric Gauge Theory from Superconnections

TL;DR

This paper reconstructs noncommutative geometric gauge theory using superconnections, deriving a generalized derivative that incorporates symmetry breaking, and links it to the Connes-Lott model's Dirac operator.

Contribution

It introduces a new generalized derivative based on superconnections that unifies curvature and symmetry breaking in noncommutative gauge theory.

Findings

Derivation of the matrix derivative from superconnections

Demonstration of spontaneous symmetry breaking via the matrix derivative

Establishment of correspondence with the Connes-Lott Dirac operator

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.