中国物理B ›› 2002, Vol. 11 ›› Issue (8): 785-789.doi: 10.1088/1009-1963/11/8/306

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

寇谡鹏   

  1. Department of Physics, Beijing Normal University, Beijing, 100875, China
  • 收稿日期:2001-12-06 修回日期:2002-01-31 出版日期:2002-08-12 发布日期:2005-06-12

The relationship between four-dimensional $\theta=\pi$ Yang－Mills theory and the two-dimensional Wess－Zumino－Novikov－Witten model

Kou Su-Peng (寇谡鹏)   

  1. Department of Physics, Beijing Normal University, Beijing 100875, China
  • Received:2001-12-06 Revised:2002-01-31 Online:2002-08-12 Published:2005-06-12

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摘要： 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.

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.

Key words: Yang－Mills field, dimensional reduction, Wess－Zumino－Novikov－Witten model

中图分类号:  (Gauge field theories)

  • 11.15.-q
11.10.Lm (Nonlinear or nonlocal theories and models) 11.30.Rd (Chiral symmetries)