We compare N=2 strings and N=4 topological strings within the framework of the sigma model approach. Being classically equivalent on a flat background, the theories are shown to lead to different geometries when put in a curved space. In contrast with the well studied Kahler geometry characterizing the former case, in the latter case a manifold has to admit a covariantly constant holomorphic two-form in order to support an N =4 twisted supersymmetry. This restricts the holonomy group to be a subgroup of SU(1,1) and leads to a Ricci-flat manifold. We speculate that the N=4 topological formalism is an appropriate framework to smooth down ultraviolet divergences intrinsic to the N=2 theory.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Mathematical Physics