Thomas Strobl: Principaloid bundles

Speaker
Thomas Strobl, Lyon U

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.