English

Heisenberg-invariant self-dual Einstein manifolds

Differential Geometry 2022-11-23 v1 High Energy Physics - Theory

Abstract

We classify all self-dual Einstein four-manifolds invariant under a principal action of the three-dimensional Heisenberg group with non-degenerate orbits. The metrics are explicit and we find, in particular, that the Einstein constant can take any value. Then we study when the corresponding (Riemannian or neutral-signature) metrics are (geodesically) complete. Finally, we exhibit the solutions of non-zero Ricci-curvature as different branches of one-loop deformed universal hypermultiplets in Riemannian and neutral signature.

Keywords

Cite

@article{arxiv.2111.11361,
  title  = {Heisenberg-invariant self-dual Einstein manifolds},
  author = {Vicente Cortés and Ángel Murcia},
  journal= {arXiv preprint arXiv:2111.11361},
  year   = {2022}
}

Comments

42 pages, no figures