Addendum to "Superconnections and Parallel Transport"

TL;DR

This paper presents an alternative construction for the parallel transport of superconnections that is independent of their specific splitting, simplifying the conceptual framework.

Contribution

It introduces a new method for superconnection parallel transport that does not depend on the particular decomposition into connection and endomorphism form.

Findings

Provides an independent construction of superconnection parallel transport.

Simplifies the understanding of superconnections by removing splitting dependence.

Enhances the theoretical framework for superconnections and their applications.

Abstract

In this addendum to our article "Superconnections and Parallel Transport" we give an alternate construction to the parallel transport of a superconnection contained in Corollary 4.4 of \cite{D1}, which has the advantage that is independent on the various ways a superconnection splits as a connection plus a bundle endomorphism valued form.