Higher Loop Bethe Ansatz for Open Spin-Chains in AdS/CFT

TL;DR

This paper develops a perturbative asymptotic Bethe ansatz for open spin-chains in AdS/CFT, analyzing boundary effects and energy spectra related to D-branes and giant gravitons.

Contribution

It introduces a novel PABA method for open spin-chains with boundary conditions in AdS/CFT, focusing on boundary S-matrices and single-magnon energy spectra.

Findings

Boundary S-matrices computed for open string excitations

Energy spectrum analyzed in the BMN limit

Application to D-brane related operators in AdS/CFT

Abstract

We propose a perturbative asymptotic Bethe ansatz (PABA) for open spin-chain systems whose Hamiltonians are given by matrices of anomalous dimension for composite operators, and apply it to two types of composite operators related to two different brane configurations. One is an AdS_4 \times S^2-brane in the bulk AdS_5 \times S^5 which gives rise to a defect conformal field theory (dCFT) in the dual field theory, and the other is a giant graviton system with an open string excitation. In both cases, excitations on open strings attaching to D-branes (a D5-brane for the dCFT case, and a spherical D3-brane for the giant graviton case) can be represented by magnon states in the spin-chains with appropriate boundary conditions, in which informations of the D-branes are encoded. We concentrate on single-magnon problems, and explain how to calculate boundary S-matrices via the PABA technique. We also discuss the energy spectrum in the BMN limit.