On AdS_5 x S^5 String S-matrix

TL;DR

This paper provides evidence supporting a Hopf algebra symmetry in the string S-matrix on AdS_5 x S^5 by showing Janik's functional equation is satisfied at strong coupling, aligning with conjectures about the dressing factor.

Contribution

It demonstrates that Janik's functional equation is solved by the dressing factor at strong coupling, supporting the conjectured Hopf algebra symmetry and the perturbative string S-matrix.

Findings

Janik's equation is satisfied by the dressing factor at strong coupling.

Supports the conjecture of a Hopf algebra symmetry in AdS_5 x S^5 strings.

Aligns the perturbative string S-matrix with the conjectured symmetry.

Abstract

Recently two interesting conjectures about the string S-matrix on AdS_5 x S^5 have been made. First, assuming the existence of a Hopf algebra symmetry Janik derived a functional equation for the dressing factor of the quantum string Bethe ansatz. Second, Hernandez and Lopez proposed an explicit form of 1/\sqrt\lambda correction to the dressing factor. In this note we show that in the strong coupling expansion Janik's equation is solved by the dressing factor up to the order of its validity. This observation provides a strong evidence in favor of a conjectured Hopf algebra symmetry for strings in AdS_5 x S^5 as well as the perturbative string S-matrix.