The geometry of N=4 twisted string

Abstract

We compare N=2 string and N=4 topological string 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 to the well studied Kaehler geometry characterising 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.

20 pages, LaTex

References in corpus (5)

• A note on N=4 supersymmetric mechanics on Kähler manifolds
• Kähler geometry and SUSY mechanics
• Restoring Lorentz Invariance in Classical N=2 String
• Complete Lagrangian formulation for N=4 topological string
• A Heterotic N=2 String with Space-Time Supersymmetry