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

Abstract

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 $2\pi$).

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

References in corpus (1)

• Vacuum Nodes in QCD at $\theta =\pi$: Exact Results

Cited by in corpus (5)

• Nahm Transform and Moduli Spaces of CPn Models on the Torus
• Theta-vacuum and large N limit in CP^{N-1} sigma models
• Vacuum Nodes and Anomalies in Quantum Theories
• Non linear sigma models and quantum spin systems
• Vacuum energy and $\theta$--vacuum