Making the hyper--K\"ahler structure of N=2 quantum string manifest
High Energy Physics - Theory
2009-11-10 v2
Abstract
We show that the Lorentz covariant formulation of N=2 string in a curved space reveals an explicit hyper--K\"ahler structure. Apart from the metric, the superconformal currents couple to a background two--form. By superconformal symmetry the latter is constrained to be holomorphic and covariantly constant and allows one to construct three complex structures obeying a (pseudo)quaternion algebra.
Cite
@article{arxiv.hep-th/0403255,
title = {Making the hyper--K\"ahler structure of N=2 quantum string manifest},
author = {S. Bellucci and A. V. Galajinsky and E. Latini},
journal= {arXiv preprint arXiv:hep-th/0403255},
year = {2009}
}
Comments
8 pages, no figures, PACS: 04.60.Ds; 11.30.Pb, Keywords: N=2 string, hyper-K\"ahler geometry. Presentation improved, references added. The version to appear in PRD