Carey, AlanJohnson, StuartMurray, Michael K2015-12-130393-0440http://hdl.handle.net/1885/87051This paper shows how to construct anomaly free world sheet actions in string theory with D-branes. Our method is to use Deligne cohomology and bundle gerbe theory to define geometric objects which are naturally associated to D-branes and connections on them. The holonomy of these connections can be used to cancel global anomalies in the world sheet action.Keywords: B-field; D-branes; Deligne cohomology200410.1016/j.geomphys.2004.02.0082015-12-12