Adjoint Fermions Induce QCD

TL;DR

This paper demonstrates that adjoint fermions on the lattice can induce QCD, showing a phase transition and drawing parallels with related models, suggesting a new way to realize QCD-like behavior.

Contribution

It introduces a lattice approach using adjoint fermions to induce QCD, analyzing phase transitions and exact solutions, expanding understanding of non-perturbative gauge theories.

Findings

A first order large-N phase transition with decreasing fermion mass.

Adjoint fermions induce QCD on the lattice.

Exact strong coupling solution similar to Kazakov--Migdal model.

Abstract

We propose to induce QCD by fermions in the adjoint representation of the gauge group SU(N_c) on the lattice. We consider various types of lattice fermions: chiral, Kogut--Susskind and Wilson ones. Using the mean field method we show that a first order large-N phase transition occurs with decreasing fermion mass. We conclude, therefore, that adjoint fermions induce QCD. We draw the same conclusion for the adjoint scalar or fermion models at large number of flavors N_f when they induce a single-plaquette lattice gauge theory. We find an exact strong coupling solution for the adjoint fermion model and show it is quite similar to that for the Kazakov--Migdal model with the quadratic potential. We discuss the possibility for the adjoint fermion model to be solvable at N_c=\infty in the weak coupling region where the Wilson loops obey normal area law.