Geodesic
$1/N$ expansion in $U(N)\times U(k)$-invariant $N\times k$ matrix chiral models $(D=2,3)$
Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 3, pp. 361-370 
A. V. Bratchikov; A. A. Deriglazov; I. V. Tyutin. $1/N$ expansion in $U(N)\times U(k)$-invariant $N\times k$ matrix chiral models $(D=2,3)$. Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 3, pp. 361-370. http://geodesic.mathdoc.fr/item/TMF_1988_75_3_a3/
@article{TMF_1988_75_3_a3,
     author = {A. V. Bratchikov and A. A. Deriglazov and I. V. Tyutin},
     title = {$1/N$~expansion in $U(N)\times U(k)$-invariant $N\times k$~matrix chiral models~$(D=2,3)$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {361--370},
     year = {1988},
     volume = {75},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_75_3_a3/}
}
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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.

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