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We compute sigma model solutions for rigidly rotating open strings suspendedbetween giant gravitons in general LLM geometries. These solutions are confinedto the LLM plane. These all have a dispersion relation for $\Delta-J$ that isconsistent with saturation of a BPS bound of the centrally extended spin chain.For the special case of circularly symmetric LLM geometries, we can furtherevaluate the amount of angular momentum $J$ carried by these strings. Thisquantity diverges for string configurations that try to move between different"coloring regions" in the LLM plane. All of these quantities have aperturbative expansion in the t'Hooft coupling. For the strings suspendedbetween 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, withthe help of the Bethe Ansatz for the $SL(2)$ sector. We thus provide additionalinformation on how the radial direction of $AdS$ arises from (open) spin chaincalculations.

Open giant magnons on LLM geometries