Proof of chiral symmetry breaking from anomaly matching in QCD-like theories

We critically reconsider the argument based on ’t Hooft anomaly matching that aims at proving chiral symmetry breaking in confining four-dimensional quantum chromodynamics-like theories with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>N</a:mi><a:mi>c</a:mi></a:msub><a:mo>&gt;</a:mo><a:mn>2</a:mn></a:math> colors and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>N</c:mi><c:mi>f</c:mi></c:msub></c:math> flavors. The main line of reasoning relies on a property of the solutions of the anomaly matching and persistent mass equations called <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>N</e:mi><e:mi>f</e:mi></e:msub></e:math>-independence. In previous works, the validity of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>N</g:mi><g:mi>f</g:mi></g:msub></g:math>-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. Published by the American Physical Society 2024