Center vortex and confinement in Yang–Mills theory and QCD with anomaly-preserving compactifications

Abstract We construct an anomaly-preserving compactification of 4D gauge theories, including SU(N) Yang–Mills theory, $\mathcal {N}=1$ supersymmetric and quantum chromodynamics (QCD), down to 2D by turning on the ’t Hooft flux through T2. This provides a new framework analytically calculate nonperturbative properties such as confinement, chiral symmetry breaking, multi-branch structure vacua. give semiclassical description these phenomena based center vortex show that it enjoys same anomaly-matching condition original theory. conjecture weak-coupling vacuum small $T^2 \times \mathbb {R}^2$ is adiabatically connected strong-coupling regime $\mathbb {R}^4$ without any phase transitions. In QCD with fundamental quarks well, we can turn either activating SU(Nf)V twist for Nf = N flavors or introducing magnetic baryon number U(1)B arbitrary flavors. both cases, center-vortex theory gives prediction consistent Lagrangian QCD.