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

## TL;DR

This paper explores how an anomalous U(1) symmetry arising from string compactification can serve as a natural global flavor symmetry, with implications for axion physics and low-energy parameters in flipped SU(5) GUT models.

## Contribution

It demonstrates the emergence of a global U(1) symmetry from an anomalous gauge U(1) in string compactification and applies it to flavor physics in a flipped SU(5) GUT model.

## Key findings

- The anomalous U(1) becomes a global symmetry below the compactification scale.
- This global symmetry can realize the 'invisible' axion.
- All low-energy parameters are computed in terms of singlet VEVs.

## Abstract

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. This global symmetry U(1)$_{\rm anom}$ is suitable for a flavor symmetry. In the simplest compactification model with the flipped SU(5) grand unification, we calculate all the low energy parameters in terms of the vacuum expectation values of the standard model singlets.