Differential K-Theory via Euclidean Field Theories

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The Stolz-Teichner program aims to describe the cocycles of certain cohomology theories in terms of supersymmetric field theories. In particular, the K-theory and the deRham cohomology of a manifold can be obtained by considering concordance classes of supersymmetric field theories of dimensions 1|1 and 0|1 over X respectively. In this talk we propose a refinement of the concordance relation so that the new equivalence classes of 1|1-dimensional Euclidean field theories over X recover the differential K-theory of the manifold. This works in arbitrary degree and we hope that the language of field theories will allow us to extend these results to the twisted and equivariant cases. This is joint work with Alexander Kahle.