The anomalous U(1) global symmetry and flavors from an SU(5) x SU(5)$'$ GUT in $Z_{12-I}$ orbifold compactification

Understand

In string compactifications, frequently there appears the anomalous U(1) gauge symmetry which belonged to E8$\times$E8 of the heterotic string.

• This anomalous U(1) gauge boson obtains mass at the compactification scale, just below $10^{18\,}$GeV, by absorbing one pseudoscalar (corresponding to the model-independent axion) from the second rank anti-symmetric tensor field $B_{MN}$.
• Below the compactification scale, there results a global symmetry U(1)$_{\rm anom}$ whose charge $Q_{\rm anom}$ is the original gauge U(1) charge.
• This is the most natural global symmetry, realizing the "invisible" axion.