Bethe ansatz equations for open spin chains from giant gravitons

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.

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

References in corpus (37)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• The N=4 SYM Integrable Super Spin Chain
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Giant Gravitons in Conformal Field Theory
• Integrability for the Full Spectrum of Planar AdS/CFT II
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
• Exact Correlators of Giant Gravitons from dual N=4 SYM
• Renormalization of twist-three operators and integrable lattice models
• Small deformations of supersymmetric Wilson loops and open spin-chains
• Integrable open spin chains from giant gravitons
• First-order flow equations for extremal black holes in very special geometry
• Completeness of the Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Analytical Bethe Ansatz for Quantum-Algebra-Invariant Spin Chains
• Anomalous dimension with wrapping at four loops in N=4 SYM
• Reflecting magnons
• Integrability and WKB solution of twist-three evolution equations
• Evolution equations for quark-gluon distributions in multi-color QCD and open spin chains
• The Bethe ansatz approach for factorizable centrally extended S-matrices
• Open Spin Chain and Open Spinning String
• Open Spin Chains in Super Yang-Mills at Higher Loops: Some Potential Problems with Integrability
• Integrable Open Spin Chains and the Doubling Trick in N = 2 SYM with Fundamental Matter
• Reflecting magnons from D7 and D5 branes
• Higher Loop Bethe Ansatz for Open Spin-Chains in AdS/CFT
• Coordinate Bethe Ansatz for the String S-Matrix
• Comments on the Boundary Scattering Phase
• Reflecting Magnon Bound States
• Open string integrability and AdS/CFT
• The Zamolodchikov-Faddeev algebra for open strings attached to giant gravitons
• The Highest Weight Property for the $S{U}_q(n)$ Invariant Spin Chains
• The Bethe Ansatz Equations for Reflecting Magnons
• Integrability and Higher Loops in AdS/dCFT Correspondence
• Fusion and Analytical Bethe Ansatz for the $A_{\n-1}^{(1)}$ Open Spin Chain
• Open Perturbatively Long-Range Integrable gl(N) Spin Chains
• Issues on magnon reflection
• On the Spectrum of the XXZ-chain at roots of unity

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• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Emergent Threebrane Lattices
• Integrable open spin-chains in AdS3/CFT2 correspondences
• Boundary finite size corrections for multiparticle states and planar AdS/CFT
• Lessons from giant gravitons on $Ad{S}_5\times T^{1,1}$
• Spectral curve for open strings attached to the Y=0 brane
• Asymptotic Bethe equations for open boundaries in planar AdS/CFT
• Revisiting the Y=0 open spin chain at one loop
• Nested algebraic Bethe ansatz for open GL(N) spin chains with projected K-matrices
• Asymptotic Bethe ansatz of ABJM open spin chain from giant graviton
• A note on open-chain transfer matrices from q-deformed su(2|2) S-matrices
• A boundary matrix for AdS/CFT SU(1|1) spin chain