Finite-size effect of \eta-deformed AdS_5 x S^5 at strong coupling

Understand

We compute Luscher corrections for a giant magnon in the \eta-deformed (AdS_5\times S^5)_{\eta} using the su(2|2)_q-invariant S-matrix at strong coupling and compare with the finite-size effect of the corresponding string state, derived previously.

• We find that these two results match and confirm that the su(2|2)_q-invariant S-matrix is describing world-sheet excitations of the \eta-deformed background.