Compatible abelian symmetries in N-Higgs-Doublet Models

TL;DR

This paper investigates how abelian symmetries can be consistently implemented across different sectors of N-Higgs-Doublet Models, providing bounds and techniques for ensuring compatibility between Higgs potential and Yukawa interactions.

Contribution

It introduces a systematic method using Smith Normal Form to analyze symmetry compatibility in NHDMs and establishes bounds on symmetry group sizes.

Findings

Equal symmetry groups in different sectors may be incompatible.

An upper bound on the size of implementable symmetry groups is derived.

Techniques for extending symmetries between sectors are developed.

Abstract

We analyze the compatibility between abelian symmetries acting in two different sectors of a theory using the Smith Normal Form method. We focus on N-Higgs-doublet models (NHDMs) and on the compatibility between symmetries in the Higgs potential and in the Yukawa interactions, which were separately analyzed previous works. It is shown that two equal (isomorphic) symmetry groups that act in two separate sectors are not necessarily compatible in the whole theory and an upper bound is found for the size of the group that can be implemented in the entire NHDM. We also develop useful techniques to analyze compatibility and extend a symmetry from one sector to another. Consequences to the supersymmetric case are briefly discussed.