Towards the spectrum of a GUT from gauge invariance

TL;DR

This paper investigates whether the Fröhlich-Morchio-Strocchi mechanism, which explains the physical spectrum in the Standard Model, applies to grand unified theories by studying a toy $SU(3)$ gauge model with two Higgs fields.

Contribution

It introduces a toy $SU(3)$ gauge theory model mimicking the Standard Model's symmetry breaking to analyze the applicability of the FMS mechanism beyond the Standard Model.

Findings

Predicted gauge-invariant spectrum at leading order

Proposed lattice gauge theory setup for testing predictions

Insights into the spectrum structure of GUT-like theories

Abstract

The description of electroweak physics using perturbation theory is highly successful. Though not obvious, this is due to a subtle field-theoretical effect, the Fr\"ohlich-Morchio-Strocchi mechanism, which links the physical spectrum to that of the elementary particles. This works because of the special structure of the standard model, and it is not a priori clear whether it works for structurally different theories. Candidates for conflicts are, e.g., grand unified theories. We study this situation in a toy model, a $SU(3)$ gauge theory with two Higgs fields and a breaking pattern $SU(3) \rightarrow SU(2) \rightarrow 1$. This mimics the weak-Higgs sector of the standard model. We determine the leading order predictions for the gauge invariant spectrum in this theory, and discuss a setup to test them using lattice gauge theory.