Open string integrability and AdS/CFT

TL;DR

This paper develops Bethe ansatz equations for open strings in AdS_5 x S^5, compares them with string spectra, and explores their implications for the AdS/CFT correspondence, especially regarding agreement and discrepancies at different loop orders.

Contribution

It introduces long-range Bethe ansatz equations for open strings and dual gauge theories, and analyzes their agreement with string spectra in the near-pp-wave limit.

Findings

Bethe ansatz equations diagonalize bosonic sectors in the near-pp-wave limit

Exact agreement between string and gauge theory at one- and two-loop orders

Disagreement at higher loops suggests missing long-range interactions in gauge theory

Abstract

We present a set of long-range Bethe ansatz equations for open quantum strings on AdS_5 x S^5 and demonstrate that they diagonalize bosonic su(2) and sl(2) sectors of the theory in the near-pp-wave limit. Results are compared with energy spectra obtained by direct quantization of the open string theory, and we find agreement in this limit to all orders in the 't Hooft coupling lambda = g_YM^2 N_c. We also propose long-range Bethe ansaetze for su(2) and sl(2) sectors of the dual N=2 defect conformal field theory. In accordance with previous investigations, we find exact agreement between string theory and gauge theory at one- and two-loop order in lambda, but a general disagreement at higher loops. It has been conjectured that the sudden mismatch at three-loop order may be due to long-range interaction terms that are lost in the weak coupling expansion of the gauge theory dilatation operator. These terms are thought to include interactions that wrap around gauge-traced operators, or around the closed-string worldsheet. We comment on the role these interactions play in both open and closed sectors of string states and operators near the pp-wave/BMN limit of the AdS/CFT correspondence.