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Ben Webster
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Ben Webster
  • 44.7k
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  • 126
  • 260

How should I think about B-fields?

So, physicists like to attach a mysterious extra cohomology class in H^2(X;C^*) to a Kahler (or hyperkahler) manifold called a "B-field." The only concrete thing I've seen this B-field do is change the Fukaya category/A-branes: when you have a B-field, you shouldn't take flat vector bundles on a Lagrangian subvariety, but rather ones whose curvature is the B-field. How should I think about this gadget?