D-branes in a topologically nontrivial B-field

Details D-branes in a topologically nontrivial B-field D-branes in a topologically nontrivial B-field

1999-09-14

arxiv.org/abs/hep-th/9909089v2

Adv.Theor.Math.Phys. 4 (2000) 127-154

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, latex. v2: typos corrected, notation improved

Scientific paper

We study global worldsheet anomalies for open strings ending on several coincident D-branes in the presence of a B-field. We show that cancellation of anomalies is made possible by a correlation between the t'Hooft magnetic flux on the D-branes and the topological class of the B-field. One application of our results is a proper understanding of the geometric nature of the gauge field living on D-branes: rather than being a connection on a vector bundle, it is a connection on a module over a certain noncommutative algebra. Our argument works for a general closed string background. We also explain why in the presence of a topologically nontrivial B-field whose curvature is pure torsion D-branes represent classes in a twisted K-theory, as conjectured by E. Witten.

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