Anomalous dimensions of heavy operators from magnon energies

We study spin chains with boundaries that are dual to open strings suspended between systems of giant gravitons and dual giant gravitons. motivated by a geometrical interpretation of the central charges of su(2|2), we propose a simple and minimal all loop expression that interpolates between the anomalous dimensions computed in the gauge theory and energies computed in the dual string theory. the discussion makes use of a description in terms of magnons, generalizing results for a single maximal giant graviton. the symmetries of the problem determine the structure of the magnon boundary reflection/scattering matrix up to a phase. we compute a reflection/scattering matrix element at weak coupling and verify that it is consistent with the answer determined by symmetry. we find the reflection/scattering matrix does not satisfy the boundary yang-baxter equation so that the boundary condition on the open spin chain spoils integrability. we also explain the interpretation of the double coset ansatz in the magnon language.