Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking

TL;DR

The paper derives a new discrete 't Hooft anomaly for massless QCD by carefully gauging the full symmetry group, including one- and two-form gauge fields, and shows that anomaly matching requires Skyrmion-mediated baryon dynamics in the ordinary chiral-symmetry breaking phase. It rules out a proposed exotic chiral-symmetry breaking phase lacking a quark bilinear condensate, as its anomaly structure cannot be matched, thereby constraining the QCD phase diagram beyond traditional inequalities. The authors also verify consistency of the new anomaly with Seiberg duality in N=1 SUSY QCD, reinforcing the robustness of the anomaly as a diagnostic for IR dynamics. Overall, the work connects topology of the vacuum manifold, baryon number realization, and discrete axial symmetry to provide a nonperturbative criterion for viable QCD vacua across zero and finite density regimes.

Abstract

We discuss consequences of the 't Hooft anomaly matching condition for Quantum Chromodynamics (QCD) with massless fundamental quarks. We derive the new discrete 't Hooft anomaly of massless QCD for generic numbers of color $N_\mathrm{c}$ and flavor $N_\mathrm{f}$, and an exotic chiral-symmetry broken phase without quark-bilinear condensate is ruled out from possible QCD vacua. We show that the $U(1)_\mathrm{B}$ baryon number symmetry is anomalously broken when the $(\mathbb{Z}_{2N_\mathrm{f}})_\mathrm{A}$ discrete axial symmetry and the flavor symmetry are gauged. In the ordinary chiral symmetry breaking, the Skyrmion current turns out to reproduce this 't Hooft anomaly of massless QCD. In the exotic chiral symmetry breaking, however, the anomalous breaking of $U(1)_\mathrm{B}$ does not take the correct form, and it is inconsistent with anomaly matching. This no-go theorem is based only on symmetries and anomalies, and thus has a wider range of applicability to the QCD phase diagram than the previous one obtained by QCD inequalities. Lastly, as another application, we check that duality of $\mathcal{N}=1$ supersymmetric QCD with $N_\mathrm{f}\ge N_\mathrm{c}+1$ satisfies the new anomaly matching.