Geodesic
Single-loop counterterm for 4-dimensional Sigma model with higher derivatives
Teoretičeskaâ i matematičeskaâ fizika, Tome 77 (1988) no. 1, pp. 42-50 Cet article a éte moissonné depuis la source Math-Net.Ru

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The most general action without dimensional parameters for the nonlinear sigma model with higher derivatives (of fourth order) is formulated in 4-dimensional space-time. A generalized Schwinger–DeWitt technique is used to calculate the single-loop counterterm up to terms proportional to the equations of motion. Conditions of single-loop finiteness are established, and renormalization-group equations for the multiplicatively renormalizable $n$-sphere case are obtained. Solutions of the renormalization-group equations with asymptotic freedom in the ultraviolet region are found. 
@article{TMF_1988_77_1_a3,
     author = {I. L. Buchbinder and S. V. Ketov},
     title = {Single-loop counterterm for 4-dimensional {Sigma} model with higher derivatives},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {42--50},
     year = {1988},
     volume = {77},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_77_1_a3/}
}
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I. L. Buchbinder; S. V. Ketov. Single-loop counterterm for 4-dimensional Sigma model with higher derivatives. Teoretičeskaâ i matematičeskaâ fizika, Tome 77 (1988) no. 1, pp. 42-50. http://geodesic.mathdoc.fr/item/TMF_1988_77_1_a3/

[1] Polyakov A., Phys. Lett., 59B:1 (1975), 79–83 | DOI | MR

[2] Belavin A. A., Polyakov A. M., Pisma v ZhETF, 22:8 (1975), 503–506

[3] Belavin A., Polyakov A., Schwartz A., Tyupkin Yu., Phys. Lett., 59B:1 (1975), 85–90 | DOI | MR

[4] Friedan D., Phys. Rev. Lett., 45:12 (1980), 1057–1060 ; Ann. Phys., 163 (1985), 318–419 | DOI | MR | DOI | MR | Zbl

[5] Alvarez-Gaume L., Freedman D., Gommun. Math. Phys., 80 (1981), 443–451 | DOI | MR

[6] Witten E., Commun. Math. Phys., 92 (1984), 455–475 | DOI | MR

[7] Skyrme T., Nucl. Phys., 31:3 (1962), 556–582 | DOI | MR

[8] Witten E., Nucl. Phys., B160:1 (1979), 57–75 ; B223:2–3 (1983), 422–445 | DOI | MR | DOI | MR

[9] Honerkamp J. et al., Nucl. Phys., B35:3 (1971), 481–492 ; B36:1 (1972), 130–140 | MR | DOI

[10] Appelquist T., Bernard C., Phys. Rev., D23:2 (1981), 425–434 | MR

[11] Spence B., Nucl. Phys., B260:3 (1985), 531–544 | DOI | MR

[12] Goroff M., Sagnotti A., Phys. Lett., 160B:1 (1985), 81–84 ; Nucl. Phys., B266:4 (1986), 709–736 | DOI | DOI

[13] Stelle K., Phys. Rev., D16:10 (1977), 953–961 | MR

[14] Fradkin E., Tseytlin A., Phys. Repts., 119:4 (1985), 233–262 | DOI | MR

[15] Avramidi I., Barvinsky A., Phys. Lett., 159B:3 (1985), 269–273 | DOI | MR

[16] Wess J., Zumino B., Phys. Lett., 37B:1 (1971), 95–97 | DOI | MR

[17] Alvarez-Gaume L. et al., Ann. Phys., 134 (1981), 85–109 | DOI | MR

[18] Braaten E. et al., Nucl. Phys., B260:4 (1985), 630–718 | DOI | MR

[19] Boulware D., Brown L., Ann. Phys., 138 (1982), 392–437 | DOI | MR

[20] Voronov B. L., Tyutin I. V., YaF, 33:10 (1981), 1137–1146

[21] Barvinsky A., Vilkovisky G., Phys. Repts., 119:1 (1985), 1–74 | DOI | MR

[22] Fradkin E., Tseytlin A., Phys. Lett., 104B:4 (1981), 377–381 ; Nucl. Phys., B201:3 (1982), 469–501 | DOI | MR | Zbl | DOI | MR

[23] Avramidi I., YaF, 44:3 (1986), 255–264 | MR

[24] Bratchikov A. V., Tyutin I. V., TMF, 66:3 (1986), 360–367 | MR