Classifying A-field and B-field configurations in the presence of D-branes

Understand

We "solve" the Freed-Witten anomaly equation, i.e., we find a geometrical classification of the B-field and A-field configurations in the presence of D-branes that are anomaly-free.

• The mathematical setting being provided by the geometry of gerbes, we find that the allowed configurations are jointly described by a coset of a certain hypercohomology group.
• We then describe in detail various cases that arise according to such classification.
• As is well-known, only under suitable hypotheses the A-field turns out to be a connection on a canonical gauge bundle.