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

TL;DR

This paper rigorously tests the quantum integrability of the AdS_5 x S^5 superstring by deriving nested light-cone Bethe equations and confirming their predictions against direct Hamiltonian diagonalization, showing perfect agreement.

Contribution

It establishes the form of nested light-cone Bethe equations for the quantum superstring and demonstrates their accuracy through detailed comparison with direct spectrum calculations.

Findings

Perfect agreement between Bethe equations and direct diagonalization results.

Validation of quantum integrability of the AdS_5 x S^5 superstring.

Analytical and numerical confirmation up to six impurity states.

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.