On the elliptic Calabi-Yau fourfold with maximal h1,1

In this paper, we explicitly construct the smooth compact base threefold for the elliptic Calabi-Yau fourfold with the largest known h1,1 = 303 148. It is generated by blowing up a smooth toric “seed” base threefold with (E8, E8, E8) collisions. The 4d F-theory compactification model over it has the largest geometric gauge group, $$ {E}_8^{2561}\times {F}_4^{7576}\times {G}_2^{20168}\times \mathrm{SU}{(2)}^{30200}, $$ 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 110015 048 ≈ 7.5 × 1045 766 different flip and flop phases of this base threefold. Moreover, we find that many other base threefolds with large h1,1 in the 4d F-theory landscape can be constructed in a similar way as well.