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.