Spin chain from membrane and the Neumann-Rosochatius integrable system

2007/06/30 by P. Bozhilov · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons #hep-th #nlin.SI

paper · pdf · doi:10.1103/physrevd.76.106003

published as Phys.Rev.D76:106003,2007 · LaTeX, 16 pages, no figures; v2: 17 pages, title changed, explanations and references added; v3: more explanations added; v4: typos fixed, to appear in Phys. Rev. D

arxiv created 2007/09/20 · openalex publication_date 2007/11/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We find membrane configurations in AdS₄\ifmmode×\else\texttimes\fiS⁷, which correspond to the continuous limit of the SU(2) integrable spin chain, considered as a limit of the SU(3) spin chain, arising in N=4 SYM in four dimensions, dual to strings in AdS₅\ifmmode×\else\texttimes\fiS⁵. We also discuss the relationship with the Neumann-Rosochatius integrable system at the level of Lagrangians, comparing the string and membrane cases.

Citations

• Geodesic flows for the Neumann-Rosochatius systems
• The circular, elliptic three-spin string from the SU(3) spin chain
• Multispin giant magnons
• Separation of variables for the classical and quantum Neumann model
• Slow evolution of nearly-degenerate extremal surfaces
• Perspective on classical strings from complex sine-Gordon solitons
• The Large-N Limit of Superconformal Field Theories and Supergravity

Cited by

• Rotating membranes in AdS 4 × M 1,1,1

Related

• Spin Chain Integrability as a Supersymmetric Gauge Duality
• The all-loop integrable spin-chain for strings on AdS₃ x S³ x T⁴: the massive sector
• Spinning strings in AdS₃ x S³ with NS-NS flux
• Spin Chains and Gauge/String Duality
• 2D Heisenberg model from rotating membrane