Superconnections and parallel transport

Florin Dumitrescu

Vol. 236 (2008), No. 2, 307–332

DOI: 10.2140/pjm.2008.236.307

Abstract

This note addresses the construction of a notion of parallel transport along superpaths arising from the concept of a superconnection on a vector bundle over a manifold M. A superpath in M is, loosely speaking, a path in M together with an odd vector field in M along the path. We also develop a notion of parallel transport associated with a connection (also know as covariant derivative) on a vector bundle over a supermanifold, which is a direct generalization of the classical notion of parallel transport for connections over manifolds.

Keywords

superconnections, parallel transport, supermanifolds, supersymmetric field theories

Mathematical Subject Classification 2000

Primary: 55N15, 53C05

Secondary: 81T60

Milestones

Received: 17 November 2007

Accepted: 17 December 2007

Published: 1 June 2008

Correction: 6 May 2012