Geodesic
$1/N$ expansion: Calculation of anomalous dimensions and mixing matrices in the order $1/N$ for $N\times p$ matrix gauge-invariant $\sigma$-model
Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 2, pp. 169-183 
A. N. Vasil'ev; M. Yu. Nalimov; Yu. R. Khonkonen. $1/N$ expansion: Calculation of anomalous dimensions and mixing matrices in the order $1/N$ for $N\times p$ matrix gauge-invariant $\sigma$-model. Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 2, pp. 169-183. http://geodesic.mathdoc.fr/item/TMF_1984_58_2_a1/
@article{TMF_1984_58_2_a1,
     author = {A. N. Vasil'ev and M. Yu. Nalimov and Yu. R. Khonkonen},
     title = {$1/N$ expansion: {Calculation} of anomalous dimensions and mixing matrices in the order $1/N$ for $N\times p$ matrix gauge-invariant $\sigma$-model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {169--183},
     year = {1984},
     volume = {58},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_58_2_a1/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In the first order in $1/N$ for arbitrary dimension $2 of space the following quantities are calculated for the $N\times p$ matrix $\sigma$ model [1] quantized by means of auxiliary scalar ($\varphi$) and vector ($B_\mu$) matrix fields: 1) the anomalous dimensions of all the fields; 2) the matrix of the anomalous dimensions of the mixed operators $\varphi$ and $B^2$ of the canonical dimension 2; 3) the matrix of the anomalous dimensions of the four mixed gauge-invariant composite operators of the type $\varphi^2$ and $G_{\mu \nu}G_{\mu \nu}$ of canonical dimension 4 determining four critical exponents $\omega$.

[1] Zakharov V. E., Mikhailov A. V., ZhETF, 74:6 (1978), 1953–1973 ; Brezin E., Itzykson C., Zinn-Justin J., Zuber J., Phys. Lett., 82B:3–4 (1979), 442–444 | MR | DOI

[2] Lüscher M., Phys. Lett., 78B:4 (1978), 465–467 ; Hikami S., Progr. Theor. Phys., 62:1 (1979), 226–233 | DOI | MR | DOI

[3] Brezin E., Hikami S., Zinn-Justin J., Nucl. Phys., B165:3 (1980), 528–544 | DOI

[4] Hikami S., Progr. Theor. Phys., 64:4 (1980), 1425–1434 | DOI | MR | Zbl

[5] Vasilev A. N., Nalimov M. Yu., TMF, 56:1 (1983), 15–30

[6] Slavnov A. A., Faddeev L. D., Vvedenie v kvantovuyu teoriyu kalibrovochnykh polei, Nauka, M., 1978 | MR

[7] Vasilev A. N., Nalimov M. Yu., TMF, 55:2 (1983), 163–175 | MR

[8] Brezin E., Le Guillou J. G., Zinn-Justin J., Phase Transitions and Critical Phenomena, eds. C. Domb, M. Green, Acad. Press, N.-Y., 1976 | MR