On the Elliptic Calabi-Yau Fourfold with Maximal $h^{1,1}$

Abstract

In this paper, we explicitly construct the smooth compact base threefold for the elliptic Calabi-Yau fourfold with the largest known $h^{1,1}=303\,148$. It is generated by blowing up a smooth toric "seed" base threefold with $(E_8,E_8,E_8)$ collisions. The 4d F-theory compactification model over it has the largest geometric gauge group, $E_8^{2\,561}\times F_4^{7\,576}\times G_2^{20\,168}\times SU(2)^{30\,200}$, and the largest number of axions, $181\,820$, in the known 4d $\mathcal{N}=1$ supergravity landscape. We also prove that there are at least $1100^{15\,048}\approx 7.5\times 10^{45\,766}$ different flip and flop phases of this base threefold. Moreover, we find that many other base threefolds with large $h^{1,1}$ in the 4d F-theory landscape can be constructed in a similar way as well.