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

TL;DR

This paper explores the implications of 't Hooft anomaly matching in massless QCD, deriving new anomalies, ruling out certain exotic phases, and confirming dualities, with a focus on the role of Skyrmions in chiral symmetry breaking.

Contribution

It derives a new discrete 't Hooft anomaly for massless QCD and demonstrates that exotic chiral symmetry breaking phases are inconsistent with anomaly matching, highlighting the importance of Skyrmions.

Findings

Exotic chiral symmetry breaking phases are ruled out by anomaly considerations.

Skyrmion currents reproduce the 't Hooft anomaly in ordinary chiral symmetry breaking.

The new anomaly matching condition is satisfied by dualities in supersymmetric QCD.

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.