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We perform a detailed test of the quantum integrability of the AdS_5 x S^5superstring in uniform light-cone gauge in its near plane-wave limit. For thiswe establish the form of the general nested light-cone Bethe equations for thequantum string from the long range psu(2,2|4) Bethe equations of Beisert andStaudacher. Moreover the scheme for translating excited string states intoBethe root excitations is given. We then confront the direct perturbativediagonalization of the light-cone string Hamiltonian in the near plane-wavelimit with the energy spectrum obtained from the general nested light-coneBethe equations in various higher rank sectors. The analysis is performed bothanalytically and numerically up to the level of six impurity states andsubsectors of maximal rank four. We find perfect agreement in all cases lendingstrong support to the quantum integrability of the AdS_5 x S^5 superstring.Comment: 34 pages, 1 figure, 12 tables, JHEP style. v2: clarifications and  references added. v3: reference added, version to be publishe

Testing the nested light-cone Bethe equations of theAdS5×S5superstring

Testing the nested light-cone Bethe equations of theAdS₅×S⁵superstring