Anomalies in orbifold field theories

C.A Scrucca,L Silvestrini,F Zwirner,M Serone

doi:10.1016/s0370-2693(01)01430-7

Abstract

We study the constraints on models with extra dimensions arising from local anomaly cancellation. We consider a five-dimensional field theory with a U(1) gauge field and a charged fermion, compactified on the orbifold S^1/(Z_2 x Z_2'). We show that, even if the orbifold projections remove both fermionic zero modes, there are gauge anomalies localized at the fixed points. Anomalies naively cancel after integration over the fifth dimension, but gauge invariance is broken, spoiling the consistency of the theory. We discuss the implications for realistic supersymmetric models with a single Higgs hypermultiplet in the bulk, and possible cancellation mechanisms in non-minimal models.

Highlights

Theories formulated in D > 4 space-time dimensions may lead to a geometrical understanding of the problems of mass generation and symmetry breaking
It is well known that the rules for the construction of consistent string-theory orbifolds are quite stringent, and automatically implement a number of consistency conditions in the corresponding effective field theories: in particular, the cancellation of gauge, gravitational and mixed anomalies
Since anomalies are infrared phenomena, if we start from a consistent string model (‘top–down’ approach), anomaly cancellation must find an appropriate description in the effective field theory

Summary

Introduction

Theories formulated in D > 4 space-time dimensions may lead to a geometrical understanding of the problems of mass generation and symmetry breaking. Another example is the four-point function involving two longitudinal and two transverse zero-mode photons, which receives a non-vanishing finite two-loop contribution controlled by the anomaly These gauge anomalies could be computed in an independent way by using their well-known relation with chiral anomalies and index theorems, which is clear in Fujikawa’s approach. In the case of a 5-D theory compactified on S1, the anomaly vanishes, since the Hilbert space splits into two identical components of opposite chirality and TrD=5 [γ5] = 0 This can be extended to an S1/(Z2 × Z′2) orbifold compactification. The elements g and g′ act chirally on the Dirac fermion ψ (gψg−1 = γ5ψ, g′ψg′−1 = −γ5ψ) and give a non-vanishing contribution Both have two fixed points, and the integrated anomaly is : TrD=5.

Supersymmetric models

Outlook