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

v4: PRD version, some clarifications; v3: Major revision that supersedes the previous versions: analysis of PMC improved significantly, proof based on downlifting and continuity moved to a new paper, simple examples added, two authors added; 41 pages, 3 figures