Quaternionic and Hyper-K\"ahler Metrics from Generalized Sigma Models
Abstract
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.
Cite
@article{arxiv.1203.1567,
title = {Quaternionic and Hyper-K\"ahler Metrics from Generalized Sigma Models},
author = {V. I. Afonso and D. Bazeia and D. J. Cirilo-Lombardo},
journal= {arXiv preprint arXiv:1203.1567},
year = {2015}
}
Comments
8 pages, two column, no figures