Strong-coupling analysis of the lattice CPN-1 models in the presence of a θ term

A θ term, which couples to topological charge, is added to the lattice CPN-1 model. The strong-coupling character expansion is developed. The series for the free energy and mass gap are, respectively, computed to tenth order and fourth order. Several features of the strong-coupling analysis emerge. One is the loss of superconfinement. Another is that, in the intermediate coupling constant region, there are indications of a transition to a deconfining phase when θ is sufficiently large. The transition is like the one which has been observed in Monte Carlo simulations of a similar lattice CPN-1 action. copyright 1997 The American Physical Society