Geodesic
Algebraic curves for integrable string backgrounds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Problems of modern theoretical and mathematical physics: Gauge theories and superstrings, Tome 272 (2011), pp. 286-298

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Many Ramond–Ramond backgrounds that arise in the AdS/CFT correspondence are described by integrable sigma-models. The equations of motion for classical spinning strings in these backgrounds can be solved quite generally by the finite-gap integration method via classical Bethe equations and algebraic curves. This construction is reviewed for general $\mathbb Z_4$ cosets and then exemplified by the backgrounds that arise in the AdS$_5$/CFT$_4$, AdS$_4$/CFT$_3$ and AdS$_3$/CFT$_2$ dualities. 
@article{TM_2011_272_a25,
     author = {K. Zarembo},
     title = {Algebraic curves for integrable string backgrounds},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {286--298},
     publisher = {mathdoc},
     volume = {272},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2011_272_a25/}
}
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K. Zarembo. Algebraic curves for integrable string backgrounds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Problems of modern theoretical and mathematical physics: Gauge theories and superstrings, Tome 272 (2011), pp. 286-298. http://geodesic.mathdoc.fr/item/TM_2011_272_a25/