Quaternionic K\"ahler and hyperK\"ahler manifolds with torsion and twistor spaces
Differential Geometry
2007-05-23 v3 High Energy Physics - Theory
Abstract
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.
Keywords
Cite
@article{arxiv.math/0112157,
title = {Quaternionic K\"ahler and hyperK\"ahler manifolds with torsion and twistor spaces},
author = {Stefan Ivanov and Ivan Minchev},
journal= {arXiv preprint arXiv:math/0112157},
year = {2007}
}
Comments
LaTeX 17 pages, Corrections in section 6, final version to appear in Crelle's Journal