Topology in Strong Coupling

The lattice $C{P}^{N-1\mathrm{}}$ model at nonzero $\theta$ is analyzed by a strong-coupling expansion. At $\theta =\pi$, $\mathrm{CP}$ is spontaneously broken and the theory ceases to confine. The $\theta$ dependence of several quantities is computed and the correlation length is shown to increase with $\theta$. Most of the results apply not only to the $C{P}^{N-1\mathrm{}}$ model (for all values of $N$) but to other two-dimensional nonlinear $\sigma$ models as well.