Higher loop Bethe ansatz for open spin-chains 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 × S 2 -brane in the bulk AdS 5 × 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 spinchains 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.

Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries

“…This boundary Yangian was further discussed in [94]. The higherloop Bethe ansatz for this class of operators was proposed in [95], see also [96] for an earlier discussion. A different derivation, which agrees with the one above, is in [97].…”

Bethe ansatz equations for open spin chains from giant gravitons

“…They also computed the one-loop boundary S-matrix, and argued that the Hamiltonian is integrable. This work was extended to two loops by Agarwal [13] (see also [14]) and by Hofman and Maldacena [15]. The latter also proposed all-loop boundary S-matrices, up to scalar factors which were subsequently found in [16,17].…”

Hidden Yangian symmetry in sigma model on squashed sphere

“…A similar geometry, that is the squashed S 3 geometry equipped with the two-form flux, can be realized as a squashed giant graviton [12] and hence the hidden symmetry found here may be useful in this issue. For example, it would be possible to consider an open string attaching on the squashed giant graviton by generalizing the works on the maximal giant graviton case [13][14][15][16]. This would be an interesting direction to be studied.…”