Quaternionic Kahler and hyperKahler manifolds with torsion and twistor spaces

摘要

The target space of a (4, 0) supersymmetric two-dimensional sigma model with a Wess-Zumino term has a connection with a totally skew-symmetric torsion and holonomy contained in Sp(n)Sp(1) (resp. Sp(n)), QKT (resp. HKT)-spaces. We study the geometry of QKT and HKT manifolds and their twistor spaces. We show that the Swann bundle of a QKT manifold admits a HKT structure with special symmetry, if and only if the twistor space of the QKT manifold admits an almost hermitian structure with totally skew-symmetric Nijenhuis tensor. In this way we connect two structures arising from quantum field theories and supersymmetric sigma models with Wess-Zumino term. [References: 43]