Frustrated symmetries in multi-Higgs-doublet models

TL;DR

This paper explores how certain symmetries in multi-Higgs-doublet models are inherently broken after electroweak symmetry breaking, drawing parallels to geometric frustration in condensed matter physics.

Contribution

It reveals that in models with more than two Higgs doublets, some symmetries are always spontaneously violated, a phenomenon linked to geometric frustration.

Findings

Symmetries in multi-Higgs-doublet models can be inherently broken after EWSB.

Certain symmetries in models with more than two doublets are always spontaneously violated.

The phenomenon is analogous to geometric frustration in condensed-matter physics.

Abstract

Within multi-Higgs-doublet models, one can impose symmetries on the Higgs potential, either discrete or continuous, that mix several doublets. In two-Higgs-doublet model any such symmetry can be conserved or spontaneously violated after the electroweak symmetry breaking (EWSB), depending on the coefficients of the potential. With more than two doublets, there exist symmetries which are always spontaneously violated after EWSB. We discuss the origin of this phenomenon and show its similarity to geometric frustration in condensed-matter physics.