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We analyze non-Higgsable clusters of gauge groups and matter that can ariseat the level of geometry in 4D F-theory models. Non-Higgsable clusters seem tobe generic features of F-theory compactifications, and give rise naturally tostructures that include the nonabelian part of the standard model gauge groupand certain specific types of potential dark matter candidates. In particular,there are nine distinct single nonabelian gauge group factors, and only fivedistinct products of two nonabelian gauge group factors with matter, including$SU(3) \times SU(2)$, that can be realized through 4D non-Higgsable clusters.There are also more complicated configurations involving more than two gaugefactors; in particular, the collection of gauge group factors with jointlycharged matter can exhibit branchings, loops, and long linear chains.

Non-Higgsable clusters for 4D F-theory models