Geodesic
Spinning string in~four-dimensional spacetime as~a~model of~$SL(2,\mathbb C)$ chiral field with anomaly.~I
Teoretičeskaâ i matematičeskaâ fizika, Tome 82 (1990) no. 2, pp. 199-207

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It is shown that the model of an open spinning (without Grassmann variables) string in dimension $\mathscr D=1+3$ is equivalent to the model of a chiral field that takes values in the group $SL(2,\mathbb C)$ and has a fixed anomaly. The Poisson structure of the theory is determined by a pair of current algebras with central charge. The action of the model is constructed in terms of the coefficients of the quadratic forms of the world surface of the string. A gauge that generalizes the standard light-cone gauge is used. 
@article{TMF_1990_82_2_a3,
     author = {S. V. Talalov},
     title = {Spinning string in~four-dimensional spacetime as~a~model of~$SL(2,\mathbb C)$ chiral field with {anomaly.~I}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {199--207},
     publisher = {mathdoc},
     volume = {82},
     number = {2},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1990_82_2_a3/}
}
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S. V. Talalov. Spinning string in~four-dimensional spacetime as~a~model of~$SL(2,\mathbb C)$ chiral field with anomaly.~I. Teoretičeskaâ i matematičeskaâ fizika, Tome 82 (1990) no. 2, pp. 199-207. http://geodesic.mathdoc.fr/item/TMF_1990_82_2_a3/