Hyper-Kähler geometry and dualization (original) (raw)

We demonstrate that in N = 8 supersymmetric mechanics with linear and nonlinear chiral supermultiplets one may dualize two auxiliary fields into physical ones in such a way that the bosonic manifold will be a hyper-Kähler one. The key point of our construction is about different dualizations of the two auxiliary components. One of them is turned into a physical one in the standard way through its replacement by the total time derivative of some physical field. The other auxiliary field which obeys the condition ∂t(Im A + Im B) = 0 is dualized through a Lagrange multiplier. We clarify this choice of dualization by presenting the analogy with a three-dimensional case.