Higher representations on the lattice: perturbative studies

TL;DR

This paper provides perturbative analytical results for lattice simulations involving Wilson fermions in higher color representations, including parameter ratios, renormalizations, and symmetry breaking patterns, aiding future numerical studies.

Contribution

It offers new perturbative calculations and insights specifically tailored for higher representation fermions on the lattice, which were previously less explored.

Findings

Computed ratio of $\\Lambda$ parameters

Determined additive fermion mass renormalization

Analyzed potential Aoki phase at finite lattice spacing

Abstract

We present analytical results to guide numerical simulations with Wilson fermions in higher representations of the colour group. The ratio of $\Lambda$ parameters, the additive renormalization of the fermion mass, and the renormalization of fermion bilinears are computed in perturbation theory, including cactus resummation. We recall the chiral Lagrangian for the different patterns of symmetry breaking that can take place with fermions in higher representations, and discuss the possibility of an Aoki phase as the fermion mass is reduced at finite lattice spacing.