# Is there an upper bound on the gauge group rank in F-theory compactifications on CY 4-folds?

It is known that in F-theory compactifications on CY 4-folds one can get gauge groups with very large ranks. The largest single factor* gauge group for compact CY 4-folds I found in the literature is the mind-blowing SO(7232) in this paper: http://arxiv.org/abs/hep-th/9706226 . One can imagine that there exist 4D compactifications of F-theory, which don't have Heterotic duals, with gauge groups that are even bigger in rank. Now, my question is whether there exists an upper bound on the ranks of single factors* in product gauge groups in either F-theory compactifications on CY 4-folds or in G2 holonomy compactifications of M-theory? An order of magnitude answer, if known, would be good enough :) .

(*) Thanks to @Luboš Motl for correcting my question!

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