Exploring SU(3)-Higgs theories

Abstract

The requirement of manifest gauge invariance leads to a conflict between perturbative and nonperturbative predictions for the low-energy spectra of grand-unified theories. These conflicts already emerge in simplified prototype models of SU(3) gauge theories with Higgs fields in different representations. We expand earlier lattice investigations on this subject and provide further support for the predicted deviations. These can be understood in terms of the Fröhlich-Morchio-Strocchi mechanism.

Possible discrepancies in the spectrum of GUT models

“…In the other cases, we consider operators with the minimum number of scalar fields. These can be constructed as tensor products with a Clebsch-Gordan construction from the basis operators [8,13,14]…”

“…This turned out be sufficient for reliable infinite-volume extrapolation. More technical details can be found in [10,13,14]. We used the results of [10] to identify useful simulation points.…”

The spectrum of GUT-like gauge-scalar models

“…As we discuss below, this mapping is in general nontrivial, which can lead to qualitative discrepancies between naive and FMS-augmented perturbation theory. The hope of all 1The situation becomes more subtle when G has multiple little groups, which could in principle allow for different 'choices' of breaking patterns: see [3] for a more detailed discussion.…”

“…[18]. We consider gauge-invariant 'building block' operators (chosen to have minimal field content in order to reduce noise) of the form [19,20] 𝑓…”

“…Gaussian distribution and accepting them according to the remaining quartic term of the potential, with the quadratic-quartic splitting chosen to maximise the acceptance probability. Further details of the implementation can be found in [3].…”