The Zamolodchikov-Faddeev Algebra for AdS₅ x S⁵ Superstring

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We discuss the Zamolodchikov-Faddeev algebra for the superstring sigma-model on AdS₅ x S⁵. We find the canonical su(2|2)² invariant S-matrix satisfying the standard Yang-Baxter and crossing symmetry equations. Its near-plane-wave expansion matches exactly the leading order term recently obtained by the direct perturbative computation. We also show that the S-matrix obtained by Beisert in the gauge theory framework does not satisfy the standard Yang-Baxter equation, and, as a consequence, the corresponding ZF algebra is twisted. The S-matrices in gauge and string theories however are physically equivalent and related by a non-local transformation of the basis states which is explicitly constructed.