U(n) Spectral Covers from Decomposition

TL;DR

This paper constructs decomposed spectral covers for bundles on elliptically fibered Calabi-Yau threefolds, revealing conditions for U(1) symmetries in heterotic and F-theory models through geometric and monodromy analysis.

Contribution

It introduces a method to decompose spectral covers and analyze monodromy reductions, enabling systematic construction of F-theory models with U(1) symmetries.

Findings

Monodromy locus factorizes with squared factors under decomposition.

Reduction of monodromy group observed in specific moduli space regions.

Explicit check of monodromy reduction in an E6 gauge theory example.

Abstract

We construct decomposed spectral covers for bundles on elliptically fibered Calabi-Yau threefolds whose structure groups are S(U(1) x U(4)), S(U(2) x U(3)) and S(U(1) x U(1) x U(3)) in heterotic string compactifications. The decomposition requires not only the tuning of the SU(5) spectral covers but also the tuning of the complex structure moduli of the Calabi-Yau threefolds. This configuration is translated to geometric data on F-theory side. We find that the monodromy locus for two-cycles in K3 fibered Calabi-Yau fourfolds in a stable degeneration limit is globally factorized with squared factors under the decomposition conditions. This signals that the monodromy group is reduced and there is a U(1) symmetry in a low energy effective field theory. To support that, we explicitly check the reduction of a monodromy group in an appreciable region of the moduli space for an $E_6$ gauge theory with (1+2) decomposition. This may provide a systematic way for constructing F-theory models with U(1) symmetries.