A talk that I once gave:
Higher field bundles for Gauge fields
talk at Operator and geometric analysis on quantum theory,
Levico Terme (Trento), Italy 15-19 September 2014
exposing basics of the higher differential geometry of higher field bundles in terms of smooth stacks appearing in gauge theory and local field theory. (A tiny motivation for differential cohomology in a cohesive topos.)
Abstract It is a well-kept secret that the fields of non-perturbative gauge theory are not in fact equivalent to sections of a field bundle, instead they are sections of a stacky “2-bundle”. Pretending this to be an ordinary bundle breaks the locality principle of the field theory, a fact that keeps being redicovered. For higher gauge fields such as a 2-form B-field, a 3-form C-field etc. this phenomenon becomes ever more pronounced and for self-dual higher gauge theory in dimension 4k+2 it is paramount. In this talk I will highlight the problem, give an introduction to its solution via “higher differential geometry” and indicate some results.
A closely related talk at the same meeting:
see also the further reviewes by Alexander Schenkel at
A bachelor thesis on this issue is
For more exposition see
For more details see
in particular section 1.2