Anomalies on orbifolds with gauge symmetry breaking

TL;DR

This paper investigates anomaly cancellation and gauge symmetry breaking in 5D orbifold models with embedded 4D chiral multiplets, analyzing different boundary conditions and their implications for localized anomalies and FI terms.

Contribution

It provides a detailed analysis of anomaly cancellation mechanisms, including the role of Chern-Simons terms, in 5D orbifold models with various boundary conditions and gauge embeddings.

Findings

Localized anomalies in Type I are canceled by bulk Chern-Simons terms.

In some Type II models, Chern-Simons terms are insufficient for anomaly cancellation.

Localized FI terms appear only at fixed points with U(1) factors.

Abstract

We embed two 4D chiral multiplets of opposite representations in the 5D N=2 $SU(N+K)$ gauge theory compactified on an orbifold $S^1/(Z_2\times Z'_2)$. There are two types of orbifold boundary conditions in the extra dimension to obtain the 4D N=1 $SU(N)\times SU(K)\times U(1)$ gauge theory from the bulk: in Type I, one has the bulk gauge group at $y=0$ and the unbroken gauge group at $y=\pi R/2$ while in Type II, one has the unbroken gauge group at both fixed points. In both types of orbifold boundary conditions, we consider the zero mode(s) as coming from a bulk $(K+N)$-plet and brane fields at the fixed point(s) with the unbroken gauge group. We check the consistency of this embedding of fields by the localized anomalies and the localized FI terms. We show that the localized anomalies in Type I are cancelled exactly by the introduction of a bulk Chern-Simons term. On the other hand, in some class of Type II, the Chern-Simons term is not enough to cancel all localized anomalies even if they are globally vanishing. We also find that for the consistent embedding of brane fields, there appear only the localized log FI terms at the fixed point(s) with a U(1) factor.