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

TL;DR

This paper extends F-theory compactification results to arbitrary bases with multiple U(1) factors, computes matter multiplicities, and constructs models with SU(5) x U(1) x U(1) gauge symmetry, ensuring anomaly cancellation.

Contribution

It generalizes previous F-theory models to arbitrary bases and introduces SU(5) x U(1) x U(1) gauge symmetry constructions with anomaly verification.

Findings

Matter hypermultiplet representations remain unchanged.

Matter multiplicities are computed for arbitrary bases.

Spectra are anomaly-free for the constructed models.

Abstract

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. We summarize the hypermultiplet matter representations, which remain the same as for the choice of the base $B=\mathbb{P}^2$ [arXiv:1306.3987], and determine their multiplicities for an arbitrary B. We also verify that the obtained spectra cancel anomalies both for U(1) x U(1) and SU(5) x U(1) x U(1).