Dyonic giant magnons inCP3: Strings and curves at finiteJ

Abstract

This paper studies giant magnons in ${\mathrm{AdS}}_{4}\ifmmode\times\else\texttimes\fi{}C{P}^{3}$ using both the string sigma model and the algebraic curve. We complete the dictionary of solutions by finding the dyonic generalization of the $C{P}^{1}$ string solution, which matches the ``small'' giant magnon in the algebraic curve, and by pointing out that the solution recently constructed by the dressing method is the ``big'' giant magnon. We then use the curve to compute finite-$J$ corrections to all cases, which for the nondyonic cases always match the Arutyunov-Frolov-Zamaklar result. For the dyonic $R{P}^{3}$ magnon we recover the ${S}^{5}$ answer, but for the small and big giant magnons we obtain new corrections.