Thomas Strobl: Principaloid bundles

Abstract

Standard gauge theories are based on principal G-bundles and associated bundles, where G is a (finite-dimensional) Lie group. However, there are gauge theories that do not fit within this framework, including the Poisson sigma model, gauged standard sigma models with a metric that does not admit isometries, and curved Yang-Mills-Higgs gauge theories. For this purpose we introduce principaloidbundles, which are based on structure Lie groupoids. These are honest fiber bundles and as such fundamentally different from principal groupoid bundles. We show that ordinary principal bundles, their associated bundles, as well as general fiber bundles are particular examples. We study connections on them, their gauge transformations, and construct the Atiyah groupoid of P, which governs its symmetries.

This is work in progress with Rafal Suszek.