An algorithm builds Calabi-Yau orientifolds and F-theory fourfold uplifts from 6d reflexive polytopes derived from orientifold data, with code in CYTools and GitHub.
Algorithmic universality in F-theory compactifica- tions
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abstract
We study universality of geometric gauge sectors in the string landscape in the context of F-theory compactifications. A finite time construction algorithm is presented for $\frac43 \times 2.96 \times 10^{755}$ F-theory geometries that are connected by a network of topological transitions in a connected moduli space. High probability geometric assumptions uncover universal structures in the ensemble without explicitly constructing it. For example, non-Higgsable clusters of seven-branes with intricate gauge sectors occur with probability above $1-1.01\times 10^{-755}$, and the geometric gauge group rank is above $160$ with probability $.999995$. In the latter case there are at least $10$ $E_8$ factors, the structure of which fixes the gauge groups on certain nearby seven-branes. Visible sectors may arise from $E_6$ or $SU(3)$ seven-branes, which occur in certain random samples with probability $\simeq 1/200$.
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In a wafer-modified Bousso-Polchinski model, 99.95% of the 532 million Calabi-Yau fourfold configurations in the Schöller-Skarke database allow vacuum energy spacings of 10^{-120} or smaller, with membrane nucleation transitions dominated by giant flux leaps under thin-wall approximations.
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Calabi-Yau Orientifold Hypersurfaces and their F-theory Uplifts
An algorithm builds Calabi-Yau orientifolds and F-theory fourfold uplifts from 6d reflexive polytopes derived from orientifold data, with code in CYTools and GitHub.
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Small Vacuum Energy and Tunneling in a Modified Bousso-Polchinski Model
In a wafer-modified Bousso-Polchinski model, 99.95% of the 532 million Calabi-Yau fourfold configurations in the Schöller-Skarke database allow vacuum energy spacings of 10^{-120} or smaller, with membrane nucleation transitions dominated by giant flux leaps under thin-wall approximations.