Heterotic Anomaly Cancellation in Five Dimensions

TL;DR

The paper investigates anomaly cancellation in five-dimensional heterotic M-theory, showing that bulk inflow constrains boundary gauge theories and yields a structured pattern in which the semi-simple part and certain type II U(1)s are anomaly-free, while type I U(1)s can be anomalous and canceled by bulk variations. It presents two complementary viewpoints: a five-dimensional gauged supergravity framework and a four-dimensional effective action perspective derived from Calabi–Yau compactifications, both yielding consistent anomaly cancellation patterns. A key result is that, on each orbifold plane, there can be at most one anomalous type I U(1) whose mixed, gravitational, and cubic anomalies are generically independent, with the mixed anomaly being universal across non-Abelian factors; a more general, non-universal structure appears in a broader 5D viewpoint. The analyses are further connected to four-dimensional results, revealing the roles of type I vs type II U(1) symmetries and the moduli (dilaton vs $T^i$) in anomaly cancellation, and leading to phenomenological implications such as Fayet–Iliopoulos terms and threshold corrections to gauge kinetic functions, relevant for model building in heterotic string/M-theory contexts.

Abstract

We study the constraints on five-dimensional N=1 heterotic M-theory imposed by a consistent anomaly-free coupling of bulk and boundary theory. This requires analyzing the cancellation of triangle gauge anomalies on the four-dimensional orbifold planes due to anomaly inflow from the bulk. We find that the semi-simple part of the orbifold gauge groups and certain U(1) symmetries have to be free of quantum anomalies. In addition there can be several anomalous U(1) symmetries on each orbifold plane whose anomalies are cancelled by a non-trivial variation of the bulk vector fields. The mixed U(1) non-abelian anomaly is universal and there is at most one U(1) symmetry with such an anomaly on each plane. In an alternative approach, we also analyze the coupling of five-dimensional gauged supergravity to orbifold gauge theories. We find a somewhat generalized structure of anomaly cancellation in this case which allows, for example, non-universal mixed U(1) gauge anomalies. Anomaly cancellation from the perspective of four-dimensional N=1 effective actions obtained from E_8xE_8 heterotic string- or M-theory by reduction on a Calabi-Yau three-fold is studied as well. The results are consistent with the ones found for five-dimensional heterotic M-theory. Finally, we consider some related issues of phenomenological interest such as model building with anomalous U(1) symmetries, Fayet-Illiopoulos terms and threshold corrections to gauge kinetic functions.