Quaternionic K\"ahler metrics associated to special K\"ahler manifolds with mutually local variations of BPS structures
Abstract
We construct a quaternionic-K\"ahler manifold from a conical special K\"ahler manifold with a certain type of mutually-local variation of BPS structures. We give global and local explicit formulas for the quaternionic-K\"ahler metric, and specify under which conditions it is positive-definite. Locally, the metric is a deformation of the 1-loop corrected Ferrara-Sabharval metric obtained via the supergravity c-map. The type of quaternionic-K\"ahler metrics we obtain are related to work in the physics literature by S. Alexandrov and S. Banerjee, where they discuss the hypermultiplet moduli space metric of type IIA string theory, with mutually local D-instanton corrections.
Keywords
Cite
@article{arxiv.2105.09011,
title = {Quaternionic K\"ahler metrics associated to special K\"ahler manifolds with mutually local variations of BPS structures},
author = {Vicente Cortés and Iván Tulli},
journal= {arXiv preprint arXiv:2105.09011},
year = {2022}
}
Comments
31 pages. Typos fixed and improved presentation based on the suggestions by the referees. Final version to appear in Annales Henri Poincar\'e