The Bethe Ansatz Equations for Reflecting Magnons

Abstract

We derive the Bethe Ansatz Equations on the half line for particles interacting through factorized $S$-matrices invariant relative to the centrally extended $su(2|2)$ Lie superalgebra and $su(1|2)$ open boundaries. These equations may be of relevance for the study of the spectrum of open strings on $Ad{S}_5\times S^5$ background attached to Y=0 giant graviton branes. An one-dimensional spin chain hamiltonian associated to this system is also derived.

23 pages; v2: corrected typos, corrected factors in equations, section 5 extended, added references. Accepted for publication in NPB

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• Integrable Wilson loops
• Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Finite size corrections for open strings/open chains in planar AdS/CFT
• Integrable open spin-chains in AdS3/CFT2 correspondences
• Y-system for Y=0 brane in planar AdS/CFT
• Boundary finite size corrections for multiparticle states and planar AdS/CFT
• Bethe ansatz for an AdS/CFT open spin chain with non-diagonal boundaries
• Bethe ansatz equations for open spin chains from giant gravitons
• On the reflection of magnon bound states
• Spectral curve for open strings attached to the Y=0 brane
• Two-Loop Integrability of ABJM Open Spin Chain from Giant Graviton
• 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
• Differential approach to on-shell scalar products in six-vertex models
• Wrapping corrections for non-diagonal boundaries in AdS/CFT
• Wrapping effects in supersymmetric gauge theories
• Reflection Maps Associated with Involutions and Factorization Problems, and Their Poisson Geometry
• A boundary matrix for AdS/CFT SU(1|1) spin chain