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

We study quantum chromodynamics including the two-index symmetric or anti-symmetric quark (QCD(Sym/ASym)) on small R-2 x 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 2d effective theory is constrained by the same anomaly of 4d 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 N = 1 supersymmetric SU(N) Yang-Mills theory.

Automated summary

This study investigates quantum chromodynamics with two-index symmetric or anti-symmetric quarks (QCD(Sym/ASym)) on small R-2 x T-2 with a suitable magnetic flux. The 't Hooft anomaly of these theories is discussed, and it is claimed that discrete chiral symmetry should be completely spontaneously broken to satisfy the anomaly matching condition. The T-2 compactification with magnetic flux preserves the 't Hooft anomaly, and the 2D effective theory is constrained by the same anomaly as the 4D QCD(Sym/ASym). The spontaneous breakdown of chiral symmetry is demonstrated using the dilute gas of center vortices, confirming the prediction of the 't Hooft anomaly. It is also found that each vacuum maintains the charge conjugation symmetry, providing support for the nonperturbative large-N orientifold equivalence between QCD(Sym/ASym) and N = 1 supersymmetric SU(N) Yang-Mills theory.