Non-Anomalous Discrete R-symmetry Decrees Three Generations

TL;DR

The paper demonstrates that a non-anomalous discrete R-symmetry larger than R-parity necessitates at least three generations of quarks and leptons in the minimal supersymmetric Standard Model embedded in grand unified theories, linking generation count to fundamental issues.

Contribution

It establishes the minimal number of generations required for anomaly-free discrete R-symmetries in GUT frameworks, connecting generation number to supersymmetry and proton decay problems.

Findings

More than two generations are needed for anomaly-free R-symmetry.

Three generations are uniquely required in certain GUT models.

Discrete R-symmetry relates to fundamental problems like SUSY breaking and proton decay.

Abstract

We show that more than two generations of quarks and leptons are required to have an anomaly free discrete R-symmetry larger than R-parity, provided that the supersymmetric Standard Model can be minimally embedded into a grand unified theory. This connects an explanation for the number of generations with seemingly unrelated problems like supersymmetry breaking, proton decay, the mu problem, and the cosmological constant through a discrete R-symmetry. We also show that three generations is uniquely required by a non-anomalous discrete R-symmetry in classes of grand unified theories such as the ones based on (semi-)simple gauge groups.