Abstract
We argue that the following three statements cannot all be true: (i) our vacuum is a type IIB / F-theory vacuum at moderate-to-large $h^{1,1}$, (ii) the $\alpha'$-expansion is controlled via the supergravity approximation, \`a la the KKLT and LVS scenarios, and (iii) there are no additional gauged sectors from seven-branes. Since nearly all known globally consistent F-theory models with the exact chiral spectrum of the Standard Model and gauge coupling unification occur at moderate $h^{1,1}$, this finding calls for new moduli stabilization scenarios or/and a rich seven-brane dark sector.
Highlights
Realizing the Standard Model of particle physics, with all moduli stabilized and all experimentally measured couplings reproduced, is an important open problem in string theory that deserves immense effort
Since most known globally consistent F-theory models with the exact chiral spectrum of the Standard Model and gauge coupling unification occur at moderate h1;1, this finding calls for new moduli stabilization scenarios or/and a rich 7-brane dark sector
While some aspects related to moduli stabilization and supersymmetry breaking are more difficult to achieve, others such as the gauge group and the chiral spectrum of the Minimal Supersymmetric Standard Model (MSSM) have been shown to have string embeddings [1,2,3,4], with the largest-to-date ensembles of global models with the exact chiral spectrum of the Standard Model being in F-theory [5]
Summary
Realizing the Standard Model of particle physics, with all moduli stabilized and all experimentally measured couplings reproduced, is an important open problem in string theory that deserves immense effort. Each of these geometries (provided a triangulation-independent numerical condition is satisfied) supports a MSSM construction without dark gauge sectors, by choosing all 7-brane stacks to wrap a particular homology class in the base, given by the anticanonical divisors, and ensuring gauge coupling unification.
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