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There have been recent advances in the construction of algebraic curves forcertain classes of string solutions in the context of the AdS/CFTcorrespondence. In this paper we obtain the Lax operators and associatedspectral curves for circular and folded string solutions in$\,\textrm{AdS}_5\times S^5$. In addition, we provide an original approach forthe reconstruction of string solutions in $\,S^3$ from their correspondingcurves.

On the algebraic curves for circular and folded strings in $\textrm{AdS}_5\times S^5$