1/N expansion in U(N) x U(k)-invariant N x k matrix chiral models (D = 2, 3)

A large class of complex N x k matrix chiral models that are exactly solvable in the limit N → ∞ is constructed. In the N → ∞ limit the phase structure of U(N) x U(k)-invariant models on the Stiefel manifolds U(N)/U(N - k) is investigated in two-dimensional (D = 2) and three-dimensional (D = 3) space-time. It is shown that in these models dynamical formation of massive vector fields is possible. Three-dimensional gauge U(N)/U(N - k) x SU(k) and U(N)/U(N - k) x U(1) models are considered, and it is shown that in them formation of both massless and massive vector fields is possible