The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
Gleb Arutyunov, Sergey Frolov, Marija Zamaklar

TL;DR
This paper constructs the Zamolodchikov-Faddeev algebra for the AdS_5 x S^5 superstring, deriving an invariant S-matrix that matches perturbative results and clarifies its relation to gauge theory formulations.
Contribution
It provides a canonical su(2|2)^2 invariant S-matrix satisfying Yang-Baxter and crossing symmetry, and shows the equivalence between string and gauge theory S-matrices via a non-local transformation.
Findings
Derived the invariant S-matrix satisfying Yang-Baxter and crossing symmetry.
Matched the near-plane-wave expansion with perturbative computations.
Established the physical equivalence of gauge and string S-matrices through a non-local basis transformation.
Abstract
We discuss the Zamolodchikov-Faddeev algebra for the superstring sigma-model on AdS_5 x S^5. 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.
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