Anomalies, Fayet-Iliopoulos terms and the consistency of orbifold field theories

TL;DR

This paper investigates the conditions for anomaly cancellation and gauge invariance in orbifold field theories, exploring the role of Fayet-Iliopoulos terms and their compatibility with supersymmetry and gauge symmetry.

Contribution

It clarifies the sufficiency of anomaly-free spectra for consistency and elucidates the relation between FI terms and anomalies in orbifold theories.

Findings

Gauge invariance can be preserved with operators breaking 5d local parity.

Localized FI terms can be added without breaking supersymmetry or gauge symmetry.

FI terms are determined by gauge invariance as boundary completions of bulk interactions.

Abstract

We study the consistency of orbifold field theories and clarify to what extent the condition of having an anomaly-free spectrum of zero-modes is sufficient to guarantee it. Preservation of gauge invariance at the quantum level is possible, although at the price, in general, of introducing operators that break the 5d local parity. These operators are, however, perfectly consistent with the orbifold projection. We also clarify the relation between localized Fayet-Iliopoulos (FI) terms and anomalies. These terms can be consistently added, breaking neither local supersymmetry nor the gauge symmetry. In the framework of supergravity the localized FI term arises as the boundary completion of a bulk interaction term: given the bulk Lagrangian the FI is fixed by gauge invariance.