Discrete R Symmetries and Anomalies

TL;DR

This paper examines discrete R symmetry anomalies, their cancellation mechanisms in string theories, and how low-energy symmetry breaking can lead to anomaly violations with implications for model building.

Contribution

It provides a heuristic explanation for anomaly cancellation via the Green-Schwarz mechanism and explores the effects of symmetry breaking on anomaly conditions in string-inspired models.

Findings

Green-Schwarz mechanism explains anomaly cancellation in heterotic strings.

Low-energy symmetry breaking can lead to non-universal discrete anomalies.

Models show different discrete charges can cause anomaly condition failures.

Abstract

We comment on aspects of discrete anomaly conditions focussing particularly on $R$ symmetries. We review the Green-Schwarz cancellation of discrete anomalies, providing a heuristic explanation why, in the heterotic string, only the "model-independent dilaton" transforms non-linearly under discrete symmetries; this argument suggests that, in other theories, multiple fields might play a role in anomaly cancellations, further weakening any anomaly constraints at low energies. We provide examples in open string theories of non-universal discrete anomalies at low energies. We then consider the fact that $R$ symmetries are necessarily broken at low energies. We exhibit dynamical models, in which fields charged under the Standard Model gauge group (for example, a doublet and a triplet) gain roughly equal masses, but where the doublet and the triplet possess different discrete charges and the low-energy anomaly conditions fail.