Open giant magnons on LLM geometries

Abstract: We compute sigma model solutions for rigidly rotating open strings suspended between giant gravitons in general LLM geometries. These solutions are confined to the LLM plane. These all have a dispersion relation for $\Delta-J$ that is consistent with saturation of a BPS bound of the centrally extended spin chain. For the special case of circularly symmetric LLM geometries, we can further evaluate the amount of angular momentum $J$ carried by these strings. This quantity diverges for string configurations that try to move between different "coloring regions" in the LLM plane. All of these quantities have a perturbative expansion in the t'Hooft coupling. For the strings suspended between AdS giants, we can compute in field theory the leading result of $J$ carried by the string via an analytic continuation of the $SU(2)$ result, with the help of the Bethe Ansatz for the $SL(2)$ sector. We thus provide additional information on how the radial direction of $AdS$ arises from (open) spin chain calculations.