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

A large class of complex $N\times k$ matrix chiral models that are exactly solvable in the limit $N\to\infty$ constructed. In the $N\to\infty$ the phase structure of $U(N)\times U(k)$-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 $U(N)/U(N-k)\times SU(k)$ and $U(N)/U(N-k)\times U(1)$ models are considered, and it is shown that in them formation of both massless and massive vector fields is possible.