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arXiv · 1908.01110

F-theory over a Fano threefold built from $A_{4}$-roots

Herbert Clemens·Stuart Raby
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Abstract

In a previous paper, the authors showed the advantages of building a $\mathbb{Z}_{2}$-action into an $F$-theory model $W_{4}/B_{3}$, namely the action of complex conjugation on the complex algebraic group with compact real form $E_{8}$. The goal of this paper is to construct the Fano threefold $B_{3}$ directly from the roots of $SU\left(5\right)$ in such a way that the action of complex conjugation is exactly the desired $\mathbb{Z}_{2}$-action and the quotient of this action on $W_{4}/B_{3}$ and its Heterotic dual have the phenomenologically correct invariants.

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Herbert Clemens, Stuart Raby. 2019-08-03. F-theory over a Fano threefold built from $A_{4}$-roots. https://arxiv.org/abs/1908.01110

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