Quaternionic and Hyper-Kähler Metrics from Generalized Sigma Models

The problem of finding new metrics of interest, in the context of SUGRA, is reduced to two stages: first, solving a generalized BPS sigma model with full quaternionic structure proposed by the authors and, second, constructing the hyper-Kähler metric, or suitable deformations of this condition, taking advantage of the correspondence between the quaternionic left-regular potential and the hyper-Kähler metric of the target space. As illustration, new solutions are obtained using generalized Q-sigma model for Wess-Zumino type superpotentials. Explicit solutions analog to the Berger's sphere and Abraham-Townsend type are given and generalizations of 4-dimensional quaternionic metrics, product of complex ones, are shown and discussed.

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