  The target space of a (4,0) supersymmetric two-dimensional sigma model with
Wess-Zumino term has a connection with 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, HKT manifold 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, thus connecting two
structures arising from quantum field theories and supersymmetric sigma models
with Wess-Zumino term.
