Catalog of electroweak scalar manifolds

TL;DR

This paper classifies all possible global structures of the electroweak scalar manifold consistent with minimal Higgs sector models, highlighting the variety of topologies and fixed points that can arise.

Contribution

It provides a comprehensive classification of electroweak scalar manifolds with minimal field content, revealing potential global structures beyond local Higgs sector analysis.

Findings

Multiple topologies of scalar manifolds identified

Existence of zero, one, or two fixed points of symmetry transformations

Physical implications of different global structures discussed

Abstract

The local structure of the Higgs sector around the vacuum does not uniquely determine its global properties. Most of the current experimental data provides only local information, which allows for a rich variety of global features, including several distinct topologies of the scalar manifold, and the existence of zero, one, or two fixed points of the symmetry transformations. Here, I provide, under general conditions, a complete classification of realizations of the electroweak symmetry with minimal field content -- the three would-be Goldstone bosons and the Higgs -- and outline some of their physical consequences.