We perform a first principles semi-classical computation of the one-loop corrections to the dispersion relation and $S$-matrix of giant magnons in $\operatorname{AdS}_5 \times S^5$ string theory. The results agree exactly with expectations based on the strong coupling expansion of the exact Asymptotic Bethe Ansatz equations. In particular we reproduce the Hernandez-Lopez term in the dressing phase.

• Heng-Yu Chen, Nick Dorey, Rui F. Lima Matos, Quantum Scattering of Giant Magnons, arXiv:0707.0668 [hep/th].