On the asymptotic states and the quantum S matrix of the $\eta$-deformed $AdS_5\times S^5$ superstring

TL;DR

This paper analyzes the integrability and S matrix of the eta-deformed AdS5xS5 superstring, showing no particle production at tree level and exploring loop corrections that reveal non-local state redefinitions linked to quantum group symmetry.

Contribution

It provides the first explicit computation of the six-point tree-level S matrix and two-loop corrections, highlighting non-local state redefinitions due to quantum group symmetry in the eta-deformed superstring.

Findings

No particle production at tree level confirms classical integrability.

Loop corrections require non-local redefinitions of two-particle states.

Two-loop logarithmic terms are represented by specific Feynman integrals.

Abstract

We investigate the worldsheet S matrix of string theory in $\eta$-deformed $AdS_5\times S^5$. By computing the six-point tree-level S matrix we explicitly show that there is no particle production at this level, as required by the classical integrability of the theory. At one and two loops we show that integrability requires that the classical two-particle states be redefined in a non-local and $\eta$-dependent way. This is a significant departure from the undeformed theory which is probably related to the quantum group symmetry of the worldsheet theory. We use generalized unitarity to carry out the loop calculations and identify a set of integrals that allow us to give a two-loop Feynman integral representation of the logarithmic terms of the two-loop S matrix. We finally also discuss aspects of the calculation of the two-loop rational terms.