Renormalization and phase transition in the quantum CPsup(N-1) model (D = 2,3)

We prove in the framework of the 1/N expansion the ultraviolet renormalizibility of the CPsup(N-1) model when D = 2, 3. It is shown that when D = 2 the model gains infrared divergences in higher orders of 1/N. When D = 3, the phase transition of second order occurs: above the critical points there exist N massive scalar charged particles and one particle corresponding to the massless isoscalar vector field, but below it there exist only N - 1 massless particles. (orig.)