The relationship between four-dimensional θ = π Yang-Mills theory and the two-dimensional Wess-Zumino-Novikov-Witten model

Used the dimensional reduction in the sense of Parisi and Sourlas, the gauge fixing term of the four-dimensional Yang-Mills field without the theta term is reduced to a two-dimensional principal chiral model. By adding the θ term (θ = π), the two-dimensional principal chiral model changes into the two-dimensional level 1 Wess-Zumino-Novikov-Witten model. The non-trivial fixed point indicates that Yang-Mills theory at θ = π is a critical theory without mass gap and confinement.