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arXiv · 2507.10169

Mysterious duality and helical line bundles on del Pezzo surfaces

Alastair King
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Abstract

Mysterious duality is a relationship, described by Vafa in 2000, between $\frac12$-BPS branes in Type II supergravity in dimension $D=d+2$ and rational curves on del Pezzo surfaces of degree $d$. We show that both sides of this correspondence can be linked to a $\mathbb{Z}_d$ grading of the Lie algebra $E_8$. 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.

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Alastair King. 2025-07-14. Mysterious duality and helical line bundles on del Pezzo surfaces. https://arxiv.org/abs/2507.10169

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