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

Understand

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.