Algebraic Curve for the SO(6) Sector of AdS/CFT

2004/10/31 by N. Beisert, Niklas Beisert, Vladimir Kazakov +3
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Nonlinear Waves and Solitons #hep-th #nlin.SI

paper · pdf · doi:10.1007/s00220-005-1528-x

published as Commun.Math.Phys.263:611-657,2006 · 58 pages, v2: minor changes, references added, v3: "length" identified in sigma model, comparison of curves improved, minor changes, v4: references added, to appear in Commun. Math. Phys

arxiv created 2005/10/03 · openalex publication_date 2006/03/03 · arxiv updated 2011/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We construct the general algebraic curve of degree four solving the classical sigma model on RxS5. Up to two loops it coincides with the algebraic curve for the dual sector of scalar operators in N=4 SYM, also constructed here. We explicitly reproduce some particular solutions.

Citations

• Strings with discrete target space
• The circular, elliptic three-spin string from the SU(3) spin chain
• A Novel Long Range Spin Chain and PlanarN=4 Super Yang-Mills
• FRACTAL STRUCTURE OF 2d—QUANTUM GRAVITY
• Higher-loop integrability in N = 4 gauge theory
• Quantum geometry of bosonic strings
• Aspects of semiclassical strings in AdS5
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Circular semiclassical string solutions on AdS5×S5
• Spin chain for quantum strings
• How Algebraic Bethe Ansatz works for integrable model
• A planar diagram theory for strong interactions
• The dilatation operator of N=4 super Yang–Mills theory and integrability
• Matrix models, topological strings, and supersymmetric gauge theories