N-Impurity Superstring Spectra Near the pp-Wave Limit

TL;DR

This paper computes superstring energy spectra near the pp-wave limit for arbitrary excitations, confirming two-loop gauge theory predictions and exploring the agreement and mismatch at higher loops, thus advancing understanding of AdS/CFT correspondence.

Contribution

It generalizes the analysis of superstring spectra to arbitrary impurity numbers and mode assignments, providing new insights into the spectrum and its relation to gauge theory.

Findings

Matching with gauge theory predictions at two loops

Mismatch observed at three loops between string and gauge theory

Agreement with Bethe ansatz in the su(2) sector to all loops

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'.