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 \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.

1+24 pages, 1 figure, typos corrected, references added, discussions on the integrability for giant gravitons modified, version to appear in JHEP

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Cited by in corpus (24)

• Small deformations of supersymmetric Wilson loops and open spin-chains
• Reflecting magnons
• Giant Gravitons - with Strings Attached (II)
• Giant Gravitons - with Strings Attached (I)
• Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries
• Hidden Yangian symmetry in sigma model on squashed sphere
• Classical Open String Integrability
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Open Spin Chains in Super Yang-Mills at Higher Loops: Some Potential Problems with Integrability
• Emergent Threebrane Lattices
• Dilatation operator and the Super Yang-Mills duals of open strings on AdS Giant Gravitons
• Comments on the Boundary Scattering Phase
• Reflecting Magnon Bound States
• Correlation Functions on the Half-BPS Wilson Loop: Perturbation and Hexagonalization
• The Zamolodchikov-Faddeev algebra for open strings attached to giant gravitons
• Deviation from tri-bimaximal mixings in two types of inverted hierarchical neutrino mass models
• Y-system for Y=0 brane in planar AdS/CFT
• Aspects of Integrability in AdS/CFT Duality
• Open Perturbatively Long-Range Integrable gl(N) Spin Chains
• Bethe ansatz equations for open spin chains from giant gravitons
• Double-helix Wilson loops: case of two angular momenta
• Revisiting the Y=0 open spin chain at one loop
• Nested algebraic Bethe ansatz for open GL(N) spin chains with projected K-matrices
• A note on open-chain transfer matrices from q-deformed su(2|2) S-matrices