1203.1567 (V. I. Afonso et al.)

Quaternionic and Hyper-Kähler Metrics from Generalized Sigma Models    [PDF]

V. I. Afonso, D. Bazeia, D. J. Cirilo-Lombardo

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-K\"{a}hler metric, or suitable deformations of this condition, taking advantage of the correspondence between the quaternionic left-regular potential and the hyper-K\"{a}hler 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.

View original: http://arxiv.org/abs/1203.1567