Finite-size effect of η-deformed AdS5 × S5 at strong coupling

We compute Lüscher corrections for a giant magnon in the η-deformed (AdS5×S5)η 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 η-deformed background.