Supersymmetry and the cohomology of (hyper) Kähler manifolds Original Research Article

The cohomology of a compact Kahler (hyperKähler) manifold admits the action of the Lie algebra so(2,1) (so(4,1)). In this paper we show, following an idea of Witten, how this action follows from supersymmetry, in particular from the symmetries of certain supersymmetric sigma models. In addition, many of the fundamental identities in Hodge-Lefschetz theory are also naturally derived from supersymmetry.