Wrapping interactions at strong coupling: The giant magnon

Abstract

We derive generalized L\"uscher formulas for finite size corrections in a theory with a general dispersion relation. For the ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ superstring these formulas encode leading wrapping interaction effects. We apply the generalized $\ensuremath{\mu}$-term formula to calculate finite size corrections to the dispersion relation of the giant magnon at strong coupling. The result exactly agrees with the classical string computation of Arutyunov, Frolov, and Zamaklar. The agreement involved a Borel resummation of all even loop orders of the BES/BHL dressing factor thus providing a strong consistency check for the choice of the dressing factor.