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Description
We present a bottom-up argument showing that the number of massless fields in six-dimensional quantum gravitational theories with eight supercharges is uniformly bounded. Specifically, we show that the number of tensor multiplets is bounded by 193, and the rank of the gauge group is restricted to 480. Given that F-theory compactifications on elliptic CY 3-folds are a subset, this provides bounds on the Hodge numbers of elliptic CY 3-folds, which are saturated by special elliptic CY 3-folds. This establishes that our bounds are sharp and also provides further evidence for the string lamppost principle. We will also briefly discuss the discrete part of the gauge group which is less understood.
