"Anomalous" U(1) Symmetry in Orbifold String Models

TL;DR

This paper investigates the conditions under which anomalous U(1) gauge symmetries arise in orbifold heterotic string models, providing a classification method and exploring their relation to discrete symmetries.

Contribution

It introduces a general procedure for classifying orbifold models with anomalous U(1) symmetries and identifies criteria for their presence or absence.

Findings

Anomalous U(1) is absent if no mixing occurs between visible and hidden sectors.

Classification reduces to models without Wilson lines.

Possible relations between anomalous U(1) and discrete R-symmetries are discussed.

Abstract

``Anomalous'' U(1) gauge symmetry with Green-Schwarz anomaly cancellation mechanism is discussed in the orbifold construction of four-dimensional heterotic string models. Some conditions are given as criteria to have ``anomalous'' U(1) in orbifold string models. In particular, ``anomalous'' U(1) is absent if the massless twisted matter has no mixing between visible and hidden sectors or if a certain type of discrete symmetries are found. We then give a general procedure for classifying orbifold models with ``anomalous'' U(1) and for identifying the ``anomalous'' U(1) basis. We illustrate our procedure in Z_3 and Z_4 orbifold models. According to our procedure, the classification of ``anomalous'' U(1) can be reduced to the classification in the absence of a Wilson line. We also discuss discrete symmetries left unbroken after the ``anomalous'' U(1) breaking. This includes a possible relation between ``anomalous'' U(1) and discrete R-symmetries.