English

Mysterious duality and helical line bundles on del Pezzo surfaces

Algebraic Geometry 2025-07-15 v1

Abstract

Mysterious duality is a relationship, described by Vafa in 2000, between 12\frac12-BPS branes in Type II supergravity in dimension D=d+2D=d+2 and rational curves on del Pezzo surfaces of degree dd. We show that both sides of this correspondence can be linked to a Zd\mathbb{Z}_d grading of the Lie algebra E8E_8. In addition, we show that the relevant rational curves correspond to `helical' line bundles, that is, line bundles that can appear in a helix on the del Pezzo surface.

Keywords

Cite

@article{arxiv.2507.10169,
  title  = {Mysterious duality and helical line bundles on del Pezzo surfaces},
  author = {Alastair King},
  journal= {arXiv preprint arXiv:2507.10169},
  year   = {2025}
}