Geodesic
Nonlinear $\sigma$ model in the case of $N\times\alpha N$ rectangular matrices in two-dimensional Euclidean space
Teoretičeskaâ i matematičeskaâ fizika, Tome 63 (1985) no. 3, pp. 367-376 
L. O. Chekhov. Nonlinear $\sigma$ model in the case of $N\times\alpha N$ rectangular matrices in two-dimensional Euclidean space. Teoretičeskaâ i matematičeskaâ fizika, Tome 63 (1985) no. 3, pp. 367-376. http://geodesic.mathdoc.fr/item/TMF_1985_63_3_a4/
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     author = {L. O. Chekhov},
     title = {Nonlinear $\sigma$ model in the case of $N\times\alpha N$ rectangular matrices in two-dimensional {Euclidean} space},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {367--376},
     year = {1985},
     volume = {63},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1985_63_3_a4/}
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The matrix nonlinear $\sigma$ model in the case of $N\times\alpha N$ rectangular matrices is considered. It is shown that in two-dimensional Euclidean space the model is renormalizable with respect to $\alpha$ and $1/N$. The fulfillment of the chirality identity is demonstrated in the operator expansion for the renormalized theory.

[1] Brezin E. et al., Commun. Math. Phys., 59:1 (1978), 35–51 | DOI | MR | Zbl

[2] Slavnov A. A., TMF, 57:1 (1983), 4–11 | MR

[3] Arefeva I. Ya., Krivoschekov V. K., Medvedev P. B., TMF, 42:3 (1980), 306–314 ; Brezin E., Hikami S., Zinn-Justine J., Nucl. Phys. B, B165 (1980), 528–550 ; Arefeva I. Ya., Azakov S. I., Dynamical rize of gauge fields in matrix $\sigma$-models, Preprint Inst. of Phys. Acad. of sc. of the Azerbaijan SSR-34, 1981, IP, Baku, 1981 | DOI

[4] Arefeva I. Ya., TMF, 29:2 (1976), 147–153 ; 31:1 (1977), 3–11 | MR | MR

[5] Arefeva I. Ya., TMF, 36:2 (1978), 159–165 ; Aref'eva I. Ya., Ann. of Phys., 117 (1979), 393–406 | MR | DOI

[6] Arefeva I. Ya., TMF, 36:1 (1978), 24–31 | MR

[7] Krivoschekov V. K., Medvedev P. B., TMF, 1984, no. 1, 3–25 ; Krivoshekov V. K., Medvedev P. B., The structure of renormalization in $\sigma$-models ($1/N$ approach), Preprint ITEP-138, 1982, ITEP, M., 1982; $1/N$ expansion in SUSY $CP^{N-1}$ model, Preprint ITEP-180, 1983, ITEP, M., 1983

[8] 't Hooft G., Nucl. Phys. B, B72:2 (1974), 461–476 | DOI