The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring

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.