Mysterious duality and helical line bundles on del Pezzo surfaces
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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