Higher representations on the lattice: perturbative studies

TL;DR

The paper develops perturbative analytic results for lattice gauge theories with Wilson fermions in higher color representations, focusing on scaling, the ratio of Λ parameters, critical mass, and bilinear renormalization, including cactus resummation. It extends the perturbative framework to arbitrary representations and analyzes how lattice artifacts interact with chiral symmetry through generalized Aoki phases described by the chiral Lagrangian for several symmetry-breaking patterns. The work identifies large representation-dependent Λ parameter ratios, provides explicit formulas for mass renormalization and Z-factors, and discusses the potential for Aoki phases in SU(2)×SU(2)→SU(2), SU(4)→SO(4), and SU(4)→Sp(4) scenarios, as well as the Dirac spectrum implications. These analytic insights are intended to guide preliminary lattice simulations of beyond-Standard-Model theories by informing parameter choices and anticipating lattice artifacts, though definitive conclusions require future numerical studies.

Abstract

We present analytical results to guide numerical simulations with Wilson fermions in higher representations of the colour group. The ratio of $Λ$ 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.