N-Impurity Superstring Spectra Near the pp-Wave Limit

TL;DR

The paper extends the near pp-wave analysis of IIB strings on AdS5 x S5 to N impurities in protected subsectors, providing direct string energy computations for arbitrary mode numbers. It confirms two-loop agreement with planar N=4 SYM predictions across SU(2) and SL(2) sectors, but reports a persistent mismatch at three loops with gauge theory, while showing all-loop agreement with a near pp-wave string Bethe ansatz in the SU(2) sector. The authors present a master formula for SU(2) energy shifts with multiple equal-mode subsets and conjecture a fermionic SU(1|1) N-impurity spectrum. They also organize the spectrum into supermultiplets and infer all-loop levels for protected subsectors, offering a framework for extending Bethe Ansatz based descriptions to higher impurities.

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 x S^5 has been shown to generate energy spectra that perfectly match, to two loops in the modified 't Hooft parameter lambda', 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 lambda', we again observe a mismatch at three loops between string and gauge theory. We find remarkable agreement to all loops in lambda', 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 lambda'.