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 $\theta$ term ($\theta=\pi$), 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 $\theta=\pi$ is a critical theory without mass gap and confinement.
Received: 06 December 2001
Revised: 31 January 2002
Accepted manuscript online:
Kou Su-Peng (寇谡鹏) The relationship between four-dimensional $\theta=\pi$ Yang－Mills theory and the two-dimensional Wess－Zumino－Novikov－Witten model 2002 Chinese Physics 11 785
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