Anomalous dimensions of heavy operators from magnon energies

de Mello Koch, R.
Tahiridimbisoa, N.H.
Mathwin, C.
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Springer Verlag
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.
1/N Expansion, AdS-CFT Correspondence, Gauge-gravity correspondence
de 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 156