The twisted story of worldsheet scattering in $\eta$-deformed $AdS_5 \times S^5$

TL;DR

This paper analyzes the integrable worldsheet scattering theory of the $ ext{eta}$-deformed $AdS_5 imes S^5$ superstring, computing the two-body S matrix at tree level and establishing its exact form consistent with quantum group symmetry.

Contribution

It provides the first explicit computation of the tree-level worldsheet S matrix for the $ ext{eta}$-deformed superstring and confirms its factorization and Yang-Baxter equation solutions, linking perturbative and exact results.

Findings

Tree-level S matrix factorizes into elementary blocks.

Exact S matrix matches perturbative expansion.

Deformed symmetry algebra is correctly identified.

Abstract

We study the worldsheet scattering theory of the $\eta$ deformation of the AdS$_\mathsf{5} \times $S$^\mathsf{5}$ superstring corresponding to the purely fermionic Dynkin diagram. This theory is a Weyl-invariant integrable deformation of the AdS$_\mathsf{5} \times $S$^\mathsf{5}$ superstring, with trigonometric quantum-deformed symmetry. We compute the two-body worldsheet S matrix of this string in the light-cone gauge at tree level to quadratic order in fermions. The result factorizes into two elementary blocks, and solves the classical Yang-Baxter equation. We also determine the corresponding exact factorized S matrix, and show that its perturbative expansion matches our tree-level results, once we correctly identify the deformed light-cone symmetry algebra of the string. Finally, we briefly revisit the computation of the corresponding S matrix for the $\eta$ deformation based on the distinguished Dynkin diagram, finding a tree-level S matrix that factorizes and solves the classical Yang-Baxter equation, in contrast to previous results.