JournalsqtVol. 2 , No. 1DOI 10.4171/qt/12

Differential forms and 0-dimensional supersymmetric field theories

  • Henning Hohnhold

    UCSD, La Jolla
  • Matthias Kreck

    Hausdorff Research Institute for Mathematics, Bonn
  • Stephan Stolz

    University of Notre Dame
  • Peter Teichner

    UC Berkeley and MPI, Bonn
Differential forms and 0-dimensional supersymmetric field theories cover

Abstract

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.