1203.3812 (Kang-Sin Choi et al.)

U(n) Spectral Covers from Decomposition    [PDF]

Kang-Sin Choi, Hirotaka Hayashi

We construct decomposed spectral covers for bundles on elliptically fibered Calabi-Yau threefolds whose structure groups are $S(U(1) \times U(4))$, $S(U(2) \times U(3))$ and $S(U(1) \times U(1) \times U(3))$ 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.

View original: http://arxiv.org/abs/1203.3812