Chiral Symmetry Breaking by Instantons

TL;DR

This review discusses how instantons in QCD lead to chiral symmetry breaking, exploring their properties, the resulting effective models, and potential confinement mechanisms, providing a comprehensive understanding of non-perturbative QCD effects.

Contribution

It provides a detailed review of the instanton vacuum in QCD, including derivations of effective models and explanations of chiral symmetry breaking mechanisms.

Findings

Instantons fluctuate according to the QCD trace anomaly.

Chiral symmetry breaking can be explained via multiple equivalent methods.

Derivation of the Nambu--Jona-Lasinio model from instantons.

Abstract

This is a review of the QCD instanton vacuum. After introducing instantons and their physical meaning, I show that the number of instantons in the vacuum fluctuates in accordance with the QCD trace anomaly. The main properties of the instanton ensemble are given. Chiral symmetry breaking by instantons is explained in three different though mathematically equivalent ways. In particular, a derivation of the Nambu--Jona-Lasinio-type model from instantons is presented, and the effective chiral lagrangian to which QCD is reduced at low momenta, is given. I end up by discussing possible confinement mechanisms.