F-Theory Compactifications with Multiple U(1)-Factors: Addendum

Understand

The purpose of this note is to extend the results obtained in [arXiv:1303.6970] in two ways.

• First, the six-dimensional F-theory compactifications with U(1) x U(1) gauge symmetry on elliptic Calabi-Yau threefolds, constructed as a hypersurface in $dP_2$ fibered over the base $B=\mathbb{P}^2$ [arXiv:1303.6970], 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) x U(1) x U(1) gauge symmetry.