Geodesic
Single-loop counterterm for 4-dimensional Sigma model with higher derivatives
Teoretičeskaâ i matematičeskaâ fizika, Tome 77 (1988) no. 1, pp. 42-50

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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},
     publisher = {mathdoc},
     volume = {77},
     number = {1},
     year = {1988},
     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/