The Line operators in the G2HDM model

TL;DR

This paper analyzes the global gauge structure of the G2HDM, focusing on how different global configurations affect line operators, charge quantization, and CP-violation, with implications for phenomenology.

Contribution

It systematically characterizes the global properties of the G2HDM, including effects on line operators and charge quantization, which were not previously detailed.

Findings

Different global structures alter Wilson, 't Hooft, and dyonic line operators.

Global structure choices influence the periodicity of CP-violating $ heta$-angles.

Minimal electric and magnetic charges depend on the quotient subgroup $\Gamma$.

Abstract

We investigate the global structure of the Gauged Two-Higgs-Doublet Model (G2HDM), a framework that extends the Standard Model by introducing a dark sector governed by the gauge symmetry $U(1)_X \times SU(2)_H$. The full gauge symmetry of the theory, including the visible sector, is given by the universal covering group $\tilde{G} = U(1)_Y \times SU(2)_L \times SU(3)_C \times U(1)_X \times SU(2)_H$. However, the true gauge group may instead be a quotient $G = \tilde{G} / \Gamma$, where $\Gamma$ is the center of $\tilde{G}$ or a subgroup thereof, leading to different global structures that cannot be distinguished by local experiments.We explore the physical implications of these global structures, analyzing their effects on Wilson, 't Hooft, and dyonic line operators, as well as the periodicity of the CP-violating $\theta$-angles associated with each group factor. Furthermore, we determine the minimal electric and magnetic charges that arise after electroweak symmetry breaking, highlighting their dependence on the choice of $\Gamma$. These findings provide a systematic characterization of the G2HDM's global properties and their potential phenomenological consequences.