Theta-vacuum: Phase Transitions and/or Symmetry Breaking at $θ= π$

Details Theta-vacuum: Phase Transitions and/or Symmetry Breaking at $θ= π$ Theta-vacuum: Phase Transitions and/or Symmetry Breaking at $θ= π$

2003-05-08

arxiv.org/abs/hep-th/0305065v2

Prog.Theor.Phys. 109 (2003) 843-851

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, 2 figures, 2 references added, final version to appear in Progr. Theor. Phys

Scientific paper

10.1143/PTP.109.843

Assuming that a quantum field theory with a $\theta$-vacuum term in the action shows non-trivial $\theta$-dependence and provided that some reasonable properties of the probability distribution function of the order parameter hold, we argue that the theory either breaks spontaneously CP at $\theta = \pi$ or shows a singular behavior at some critical $\theta_c$ between 0 and $\pi$. This result, which applies to any model with a pure imaginary contribution to the euclidean action consisting in a quantized charge coupled to a phase, as QCD, is illustrated with two simple examples; one of them intimately related to Witten's result on SU(N) in the large $N$ limit.

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