Abstract
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.
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