De Rham model for string topology

String topology of Chas and Sullivan deals with an ample family of algebraic operations on the ordinary and equivariant homologies of the free loop space of a simply connected manifold. The most important of these is a graded commutative associative product on the shifted homology of the free loop space which generalizes the Pontrjagin product on the based loop space. We use the theory of iterated integrals to give a new proof of the main theorem of the string topology on the Hochschild cohomology incarnation of the Chas-Sullivan product, and its “brane” generalization.