Bi-HKT and bi-Kähler supersymmetric sigma models (Q2804965)

Physicists refer to Lagrangian theories in which the bosonic fields carry the interpretation of coordinates on a manifold (the target space) as sigma models. The dimension of the domain of the fields is referred to as the dimensionality of the sigma model. Imposing symmetries on the model necessitates considering target spaces endowed with appropriate geometric structures. Fedoruk and Smilga study one dimensional supersymmetric sigma models (supersymmetric quantum mechanics), relatives of the more thoroughly studied 2d sigma models that feature prominently in string theory. Imposing extended supersymmetry on the model proves less restrictive in one dimension. The geometry studied in this paper, referred to as CKT (Clifford Kähler with torsion), is a generalization of the HKT (hyper-Kähler with torision) geometries studied in two dimensions for models with (4,0) supersymmetry. The authors carefully distill the definition of CKT structures from the physics literature, and situate them in the class of hypercomplex manifolds. They discuss how to write down Lagrangians with this structure, introducing the notion of mirror multiplets. They furthermore discuss how in favorable circumstances, a Hamiltonian reduction of the CKT models to twisted Kähler models, which have already appeared in the literature, is possible.