On the Proof of Chiral Symmetry Breaking from Anomaly Matching in QCD-like Theories

TL;DR

This paper rigorously proves the conditions under which anomaly matching implies chiral symmetry breaking in QCD-like theories, clarifying previous assumptions and extending validity to a broad spectrum of composite fermions.

Contribution

It provides a detailed proof of the $N_f$-independence property in anomaly matching, clarifying its validity conditions in QCD-like theories.

Findings

Proved the $N_f$-independence property rigorously.

Extended anomaly matching validity to include baryons and exotics.

Clarified conditions for chiral symmetry breaking in confining theories.

Abstract

We critically reconsider the argument based on 't Hooft anomaly matching that aims at proving chiral symmetry breaking in confining four-dimensional QCD-like theories with $N_c>2$ colors and $N_f$ flavors. The main line of reasoning relies on a property of the solutions of the anomaly matching and persistent mass equations called $N_f$-independence. In previous works, the validity of $N_f$-independence was assumed based on qualitative arguments, but it was never proven rigorously. We provide a detailed proof and clarify under which (dynamical) conditions it holds. Our results are valid for a generic spectrum of massless composite fermions including baryons and exotics.