Testing the nested light-cone Bethe equations of the AdS_5 x S^5 superstring

Abstract

We perform a detailed test of the quantum integrability of the AdS_5 x S^5 superstring in uniform light-cone gauge in its near plane-wave limit. For this we establish the form of the general nested light-cone Bethe equations for the quantum string from the long range psu(2,2|4) Bethe equations of Beisert and Staudacher. Moreover the scheme for translating excited string states into Bethe root excitations is given. We then confront the direct perturbative diagonalization of the light-cone string Hamiltonian in the near plane-wave limit with the energy spectrum obtained from the general nested light-cone Bethe equations in various higher rank sectors. The analysis is performed both analytically and numerically up to the level of six impurity states and subsectors of maximal rank four. We find perfect agreement in all cases lending strong support to the quantum integrability of the AdS_5 x S^5 superstring.

34 pages, 1 figure, 12 tables, JHEP style. v2: clarifications and references added. v3: reference added, version to be published

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Cited by in corpus (9)

• Foundations of the AdS_5 x S^5 Superstring. Part I
• Classical integrability and quantum aspects of the AdS(3) x S(3) x S(3) x S(1) superstring
• Near BMN dynamics of the AdS(3) x S(3) x S(3) x S(1) superstring
• A Yangian Double for the AdS/CFT Classical r-matrix
• Factorized world-sheet scattering in near-flat AdS_5 x S^5
• The AdS(4) x CP(3) string and its Bethe equations in the near plane wave limit
• Classical and quantum integrability in AdS(2)/CFT(1)
• Review of AdS/CFT Integrability, Chapter II.2: Quantum Strings in AdS5xS5
• On the worldsheet theory of the type IIA AdS(4) x CP(3) superstring