Generic HKT geometries in the harmonic superspace approach

International audienceWe explain how a generic hyper-Kähler with torsion (HKT) geometry can be derived using the language of N=4 supersymmetric quantum mechanics. To this end, one should consider a Lagrangian involving several (4, 4, 0) multiplets defined in harmonic superspace and subject to nontrivial harmonic constraints. Conjecturally, this general construction presented in the paper of F. Delduc and E. Ivanov [Nucl. Phys. B 855, 815 (2012)] gives a complete classification of all HKT geometries. Each such geometry is generated by two different functions (potentials) of a special type that depend on harmonic superfields and on harmonics. Given these two potentials, one can derive the vielbeins, metric, connections, and curvatures, but this is not so simple: one should solve rather complicated differential equations. We illustrate the general construction by giving a detailed derivation of the metric for hyper-Kähler Taub-NUT manifolds. In the generic case, we arrive at an HKT geometry. In this paper, we give a simple proof of this assertion