N-impurity superstring spectra near the pp-wave limit

Abstract

The complicated non-linear sigma model that characterizes the first finite-radius curvature correction to the pp-wave limit of IIB superstring theory on AdS 5 × S 5 has been shown to generate energy spectra that perfectly match, to two loops in the modified 't Hooft parameter λ ′ , finite R-charge corrections to anomalous dimension spectra of large- R N = 4 super-Yang–Mills theory in the planar limit. This test of the AdS/CFT correspondence has been carried out for the specific cases of two and three string excitations, which are dual to gauge theory R-charge impurities. We generalize this analysis on the string side by directly computing string energy eigenvalues in certain protected sectors of the theory for an arbitrary number of worldsheet excitations with arbitrary mode-number assignments. While our results match all existing gauge theory predictions to two-loop order in λ ′ , we again observe a mismatch at three loops between string and gauge theory. We find remarkable agreement to all loops in λ ′ , however, with the near pp-wave limit of a recently proposed Bethe ansatz for the quantized string Hamiltonian in the su ( 2 ) sector. Based on earlier two- and three-impurity results, we also infer the full multiplet decomposition of the N-impurity superstring theory with distinct mode excitations to two loops in λ ′ .