Semiclassics with 't Hooft flux background for QCD with $2$-index quarks

TL;DR

This paper investigates QCD with two-index quarks on a compactified space with magnetic flux, demonstrating chiral symmetry breaking and supporting large-N equivalence with supersymmetric Yang-Mills theory through anomaly analysis and vortex configurations.

Contribution

It introduces a semiclassical approach to analyze QCD(Sym/ASym) with magnetic flux, revealing chiral symmetry breaking and confirming large-N equivalence with supersymmetric theories.

Findings

Chiral symmetry is spontaneously broken in the studied setup.

Charge conjugation symmetry remains unbroken in each vacuum.

Supports nonperturbative large-N orientifold equivalence.

Abstract

We study quantum chromodynamics including the two-index symmetric or anti-symmetric quark (QCD(Sym/ASym)) on small $\mathbb{R}^2\times T^2$ with a suitable magnetic flux. We first discuss the 't Hooft anomaly of these theories and claim that discrete chiral symmetry should be spontaneously broken completely to satisfy the anomaly matching condition. The $T^2$ compactification with the magnetic flux preserves the 't Hooft anomaly, and the $2$d effective theory is constrained by the same anomaly of $4$d QCD(Sym/ASym). We demonstrate the spontaneous breakdown of chiral symmetry using the dilute gas of center vortices, which confirms the prediction of the 't Hooft anomaly. We also find that each vacuum maintains the charge conjugation symmetry, and this gives affirmative support for the nonperturbative large-$N$ orientifold equivalence between QCD(Sym/ASym) and $\mathcal{N}=1$ supersymmetric $SU(N)$ Yang-Mills theory.