Line Operators in the Standard Model

TL;DR

The paper clarifies how the Standard Model's gauge-group global structure, encoded by G = \tilde{G}/Γ with Γ ⊆ Z6, alters the spectrum of nonlocal line operators and the periodicities of theta angles. Building on the line-operator framework of Aharony–Seiberg–Tachikawa, it classifies electric, magnetic, and dyonic lines for each Γ and analyzes how θ angles shift the operator spectrum via the Witten effect, including after electroweak symmetry breaking. It finds that Γ controls which electric lines survive, permits fractional magnetic charges, and changes the range of θ_em, with Γ = Z3 or Z6 implying color-charged monopoles and a U(3) low-energy gauge structure. Despite these changes being formal for flat-space observables, the authors discuss potential physical implications in topologically nontrivial spacetimes and scenarios involving gravity, motivating further exploration of the SM's global gauge structure.

Abstract

There is an ambiguity in the gauge group of the Standard Model. The group is $G = SU(3) \times SU(2) \times U(1)/Γ$, where $Γ$ is a subgroup of ${\bf Z}_6$ which cannot be determined by current experiments. We describe how the electric, magnetic and dyonic line operators of the theory depend on the choice of $Γ$. We also explain how the periodicity of the theta angles, associated to each factor of $G$, differ.

Figures (1)

• Figure 1: The spectrum of line operators for: a) $SU(3)$; b) $SU(3)/{\bf Z}_3$ at $\theta=0$; c) $SU(3)/{\bf Z}_3$ at $\theta=2\pi$; d) $SU(3)/{\bf Z}_3$ at $\theta=4\pi$.