Geodesic
Geometry of~dual two-dimensional nonlinear $\sigma$~models
Teoretičeskaâ i matematičeskaâ fizika, Tome 84 (1990) no. 2, pp. 173-180

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Geometrical aspects of duality in two-dimensional nonlinear $\sigma$ models are considered. The metric and torsion potential are found explicitly for the dual versions of two theories: a) the dimensional reduction to $d=2$ of the self-interaction of an $N=2$, $d=4$ tensor supermultiplet represented by a sum of an “unimproved” (linear) and “improved” (nonlinear) free action, b) the two-dimensional Freedman–Townsend model. The single- and two-loop $\beta$ functions have been calculated (on a computer). 
@article{TMF_1990_84_2_a1,
     author = {S. V. Ketov and K. E. Osetrin and Ya. S. Prager},
     title = {Geometry of~dual two-dimensional nonlinear $\sigma$~models},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {173--180},
     publisher = {mathdoc},
     volume = {84},
     number = {2},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1990_84_2_a1/}
}
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S. V. Ketov; K. E. Osetrin; Ya. S. Prager. Geometry of~dual two-dimensional nonlinear $\sigma$~models. Teoretičeskaâ i matematičeskaâ fizika, Tome 84 (1990) no. 2, pp. 173-180. http://geodesic.mathdoc.fr/item/TMF_1990_84_2_a1/