We apply the path-integral formalism to compute the anomalies in general orbifold gauge theories (including possible nontrivial Scherk-Schwarz boundary conditions) where a gauge group [Formula Presented] is broken down to subgroups [Formula Presented] at the fixed points [Formula Presented] Bulk and localized anomalies, proportional to [Formula Presented] do generically appear from matter propagating in the bulk. The anomaly zero mode that survives in the four-dimensional effective theory should be canceled by localized fermions [except possibly for mixed [Formula Presented] anomalies]. We examine in detail the possibility of canceling localized anomalies by the Green-Schwarz mechanism involving two- and four-forms in the bulk. The four-form can only cancel anomalies which do not survive in the 4D effective theory: they are called globally vanishing anomalies. The two-form may cancel a specific class of mixed [Formula Presented] anomalies. Only if these anomalies are present in the 4D theory does this mechanism spontaneously break the [Formula Presented] symmetry. The examples of five- and six-dimensional [Formula Presented] orbifolds are considered in great detail. In five dimensions the Green-Schwarz four-form has no physical degrees of freedom and is equivalent to canceling anomalies by a Chern-Simons term. In all other cases, the Green-Schwarz forms have some physical degrees of freedom and leave some nonrenormalizable interactions in the low energy effective theory. In general, localized anomaly cancellation imposes strong constraints on model building. © 2003 The American Physical Society.
|Journal||Physical Review D - Particles, Fields, Gravitation and Cosmology|
|Publication status||Published - 1 Jan 2003|