Vacuum structure of CP^N sigma models at theta=pi

Details Vacuum structure of CP^N sigma models at theta=pi Vacuum structure of CP^N sigma models at theta=pi

1997-12-12

arxiv.org/abs/hep-th/9712126v1

Phys.Rev.Lett. 80 (1998) 234-237

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, revtex, to appear in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.80.234

We show that parity symmetry is not spontaneously broken in the CP^N sigma model for any value of N when the coefficient of the $\theta$--term becomes $\theta=\pi$ (mod $2\pi$). The result follows from a non-perturbative analysis of the nodal structure of the vacuum functional $\psi_0(z)$. 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 $\theta=\pi$ (mod $2\pi$).

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