de Mello Koch, R.Tahiridimbisoa, N.H.Mathwin, C.2017-04-132017-04-132016-03de Mello Koch, R. Tahiridimbisoa, N.H and Mathwin, C. 2016. Anomalous dimensions of heavy operators from magnon energies. Journal of High Energy Physics 2016 (3) : Article number 1561126-6708 (Print)1029-8479 (Online)http://hdl.handle.net/10539/22393We 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.en© 2016 de Mello Koch, R. et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0).1/N ExpansionAdS-CFT CorrespondenceGauge-gravity correspondenceArticle