2001/12/31 by Stefan Ivanov, Ivan Minchev
Mathematics · Physics and Astronomy · #math.DG #hep-th #msc:53C25
published as J. Reine Angew. Math. 567 (2004), 215-233 · LaTeX 17 pages, Corrections in section 6, final version to appear in Crelle's Journal
arxiv created 2003/09/11 · arxiv updated 2009/11/30
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.