F-theory compactifications with multiple U(1)-factors: Addendum

The purpose of this note is to extend the results obtained in [1] in two ways. First, the six-dimensional F-theory compactifications with U(1)xU(1) gauge symmetry on elliptic Calabi-Yau threefolds, constructed as a hypersurface in dP2 fibered over the base B = ℙ2 [1] , are generalized to Calabi-Yau threefolds elliptically fibered over an arbitrary two-dimensional base B. While the representations of the matter hypermultiplets remain unchanged, their multiplicities are calculated for an arbitrary B . Second, for a specific non-generic subset of such Calabi-Yau threefolds we engineer SU(5)xU(1)xU(1) gauge symmetry. We summarize the hypermultiplet matter representations, which remain the same as for the choice of the base B = ℙ2 [2], and determine their multiplicities for an arbitrary B. We also verify that the obtained spectra cancel anomalies both for U(1)xU(1) and SU(5)xU(1)xU(1). © SISSA 2013.