We show that closed differential forms on a smooth manifold X can be interpreted as topological (respectively Eudlidean) supersymmetric field theories of dimension 0|1 over X. As a consequence, concordance classes of such field theories are shown to represent de Rham cohomology. The main contribution of this paper is to make all new mathematical notions regarding supersymmetric field theories precise.
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Henning Hohnhold, Matthias Kreck, Stephan Stolz, Peter Teichner, Differential forms and 0-dimensional supersymmetric field theories. Quantum Topol. 2 (2011), no. 1, pp. 1–41DOI 10.4171/QT/12