Quaternionic K'ahler and hyperK'ahler manifolds with torsion and twistor spaces

摘要

The target space of a (4,0) supersymmetric two-dimensional sigma model withWess-Zumino term has a connection with totally skew-symmetric torsion andholonomy contained in Sp(n)Sp(1) (resp. Sp(n)), QKT (resp. HKT)-spaces. Westudy the geometry of QKT, HKT manifold and their twistor spaces. We show thatthe Swann bundle of a QKT manifold admits a HKT structure with special symmetryif and only if the twistor space of the QKT manifold admits an almost hermitianstructure with totally skew-symmetric Nijenhuis tensor, thus connecting twostructures arising from quantum field theories and supersymmetric sigma modelswith Wess-Zumino term.