Abstract
We generalize to dimension the notion of string structure and discuss the related obstruction. We apply our results to a model of bosonic -branes propagating on a principal -bundle, coupled to a Yang--Mills field and an antisymmetric tensor field and in the presence of a Wess-Zumino term in the Lagrangian. We construct the quantization line bundle and discuss the action of background gauge transformations on wave functions.
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