Vacuum structure of CPⁿ sigma models at theta=pi

Original · EN

We show that parity symmetry is not spontaneously broken in the CPⁿ sigma model for any value of N when the coefficient of the θ--term becomes θ=π (mod 2π). The result follows from a non-perturbative analysis of the nodal structure of the vacuum functional ψ₀(z). The dynamical role of sphalerons turns out to be very important for the argument. The result introduces severe constraints on the possible critical behavior of the models at θ=π (mod 2π).