The spectrum of nonabelian gauge theories cannot be described in terms of elementary particles,
and so must be constructed from gauge-invariant composite operators, even in the presence of
a Brout–Englert–Higgs effect. This leads to qualitative discrepancies in the prediction of the
spectrum between perturbation theory and a full non-perturbative treatment in many theories.
This is especially noticeable for GUTs. We present results corroborating this general statement
using lattice simulations for a “GUT-like” toy theory, SU(3) Yang–Mills theory coupled to a Higgs
field in the fundamental representation. Despite the apparent simplicity of the model, we find a
rich spectrum with some previously unseen features. We also outline the next steps required to
generate a large operator basis to extend this investigation to more realistic GUTs.