Bundle gerbes are the geometric objects which describe B-fields in string theory. Their sections, in turn, are the (twisted) Chan-Paton bundles that model the K-theory charges of D-branes. While this describes the topological part of a spacetime geometry in string theory, the configuration space of strings consists of loop and path spaces. On these spaces, the same geometry takes a different form; we show that it translates to bundles of algebras and bimodules that generalise coloured, knowledgeable Frobenius algebras. From a yet different perspective, the perturbative interactions of strings are encoded in a smooth, open-closed functorial field theory on the background manifold.

In this talk, based on a collaboration with Konrad Waldorf, we will employ the 2-categorical structure of bundle gerbes to provide concrete constructions that relate the spacetime, path space, and functorial field theory perspectives on B-fields and D-branes in bosonic string theory.

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