Bethe ansatz equations for open spin chains from giant gravitons

TL;DR

This paper derives Bethe ansatz equations for open spin chains associated with giant gravitons, demonstrating integrability and providing explicit eigenvalue solutions in various sectors.

Contribution

It offers a direct proof of integrability for the open spin chain in SU(2) and SU(3) sectors and proposes BAEs for the full SO(6) sector, connecting with recent all-loop proposals.

Findings

Constructed transfer matrices confirming integrability.

Derived Bethe ansatz equations for SU(2), SU(3), and SO(6) sectors.

Showed agreement with recent all-loop BAEs in the weak-coupling limit.

Abstract

We investigate the open spin chain describing the scalar sector of the Y=0 giant graviton brane at weak coupling. We provide a direct proof of integrability in the SU(2) and SU(3) sectors by constructing the transfer matrices. We determine the eigenvalues of these transfer matrices in terms of roots of the corresponding Bethe ansatz equations (BAEs). Based on these results, we propose BAEs for the full SO(6) sector. We find that, in the weak-coupling limit, the recently-proposed all-loop BAEs essentially agree with those proposed in the present work.