Classifying A-field and B-field configurations in the presence of D-branes - Part II: Stacks of D-branes

Understand

In the paper arXiv:0810.4291 we have shown, in the context of type II superstring theory, the classification of the allowed B-field and A-field configurations in the presence of anomaly-free D-branes, the mathematical framework being provided by the geometry of gerbes.

• Here we complete the discussion considering in detail the case of a stack of D-branes, carrying a non-abelian gauge theory, which was just sketched in the previous paper.
• In this case we have to mix the geometry of abelian gerbes, describing the B-field, with the one of higher-rank bundles, ordinary or twisted.
• We describe in detail the various cases that arise according to such a classification, as we did for a single D-brane, showing under which hypoteses the A-field turns out to be a connection on a canonical gauge bundle.