Relating ’t Hooft anomalies of 4d pure Yang-Mills and 2d ℂℙ N− 1 model

Abstract

Abstract It has recently been shown that a center-twisted compactification of the four-dimensional pure SU(N) Yang-Mills theory on a three-torus gives rise to the twodimensional ℂℙ N− 1-model on a circle with a flavor-twisted boundary condition. We verify the consistency of this statement non-perturbatively at theta angle θ = π, in terms of the mixed ’t Hooft anomalies for flavor symmetries and the time-reversal symmetry. This provides further support for the approach to the confinement of four-dimensional Yang-Mills theory from the two-dimensional ℂℙ N− 1-model.

Keywords

• Anomalies in Field and String Theories
• Confinement