Chiral symmetry breaking and confinement: separating the scales

TL;DR

This paper reviews the mechanisms of chiral symmetry breaking and confinement in gauge theories, proposing models and candidate theories where these phenomena occur at widely separated energy scales, which can be tested via lattice simulations.

Contribution

It identifies specific gauge theories with matter representations that maximize the separation between chiral symmetry breaking and confinement scales, and suggests lattice testing of these models.

Findings

Potential separation of scales up to a factor of 20 in certain theories.

Candidate theories include SU(2) with a Weyl quark in the 4-dimensional representation.

Multi-representation theories may exhibit distinct condensation and confinement scales.

Abstract

We review arguments that chiral symmetry breaking is triggered when the quark bilinear condensate's dimension passes through one ($\gamma=1$). This is supported by gap equations and more recently holographic models. Confinement may then be a separate property of the pure Yang-Mills theory below the scale of the dynamically generated quark mass, occurring at the scale of the pole in the deep IR running. Here, we use perturbative results for the running of the gauge coupling and $\gamma$ in asymptotically free SU($N_c$) gauge theories with matter in higher dimension representations to seek the best candidate theories where confinement and chiral symmetry breaking can be maximally separated. For example, SU(2) gauge theory with a single Weyl quark in the $S_3$ (dimension 4) representation may have a factor of 20 separation in scale. Such a theory could be simulated on the lattice to test the separation. We also propose studying multi-representation theories where the higher dimension representation forms a condensate at one scale that can be quite separate from the condensation scale of the second representation matter. The confinement scale would presumably be below the second scale. For example, SU(3) gauge theory with a Weyl adjoint fermion and ten fundamental quarks may have a separation of a factor of 20 also.