Instabilities of bulk fields and anomalies on orbifolds

Abstract

Bulk matter modes of higher-dimensional models generically become unstable in the presence of additional matter multiplets at the branes. This quantum instability is driven by localized Fayet–Iliopoulos terms that attract the bulk zero modes towards the boundary branes. We study this mechanism in the framework of a 5-dimensional S 1/ Z 2 orbifold and give conditions for the various possibilities of localization of (chiral) zero modes. This mechanism is quite relevant for realistic model building, as the standard model contains U(1) hypercharge with potentially localized FI-terms. The analysis is closely related to localized anomalies in higher-dimensional gauge theories. Five-dimensional gauge invariance of the effective action determines the anomaly constraints and fixes the normalization of Chern–Simons terms. The localization of the bulk modes does not effect the anomaly cancellation globally, but the additional heavy Kaluza–Klein modes of the bulk fields may cancel the Chern–Simons terms. We discuss also the potential appearance of the parity anomaly that might render the construction of some orbifold models inconsistent.