October 2, 2025Open Access

Mysterious duality and helical line bundles on del Pezzo surfaces

Key Points

Duality can be connected to the Lie algebra E8, creating a deeper understanding of its structure.
Rational curves are shown to correspond to helical line bundles on del Pezzo surfaces.
The analysis uncovers a relationship between half-BPS branes and geometry in supergravity contexts.
This work enhances the understanding of mathematical physics by uniting abstract algebra and geometry.

Abstract

Mysterious duality is a relationship, described by Vafa in 2000, between 12-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 Zd grading of the Lie algebra E₈. 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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Cite This Study

Alastair J. King (Mon,) studied this question.

synapsesocial.com/papers/68de6f3f83cbc991d0a22d8c https://doi.org/https://doi.org/10.48550/arxiv.2507.10169

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