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# Advances in Theoretical and Mathematical Physics

## Volume 26 (2022)

### Number 2

### $F$-theory over a Fano threefold built from $A_4$-roots

Pages: 325 – 370

DOI: https://dx.doi.org/10.4310/ATMP.2022.v26.n2.a3

#### Authors

#### 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 $SU(5)$ 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.

S.R. acknowledges partial support from Department of Energy grant DE-SC0011726.

Published 27 December 2022