Bethe ansatz equations for open spin chains from giant gravitons

Details Bethe ansatz equations for open spin chains from giant gravitons Bethe ansatz equations for open spin chains from giant gravitons

2009-03-09

arxiv.org/abs/0903.1646v3

JHEP 0905:100,2009

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, v2: minor improvements and clarifications; v3: changes reflecting those in arXiv:0902.1681, and references added

Scientific paper

10.1088/1126-6708/2009/05/100

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.

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