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

TL;DR

We construct the Zamolodchikov-Faddeev algebra for the AdS5×S5 string and show the canonical su(2|2)² invariant S-matrix is fixed by symmetry to satisfy Yang–Baxter, unitarity, hermitian analyticity, and crossing, up to a scalar factor. The full S-matrix is a tensor product of two su(2|2) S-matrices, with the string basis yielding the standard Yang–Baxter equation, while the gauge-theory (Beisert) S-matrix is twisted and related by a non-local basis transformation. The near plane–wave expansion reproduces leading perturbative results, and the formalism naturally encodes worldsheet momentum as a central charge with nontrivial braiding in multi-particle states. This work places the AdS5×S5 string within the familiar framework of integrable massive models, clarifies the role of basis choices, and points to Bethe-ansatz and finite-size approaches for the dual gauge/string system.

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.