Bethe ansatz for a quantum supercoset sigma model

2005/08/31 by Nelia Mann, Joseph Polchinski, Joe Polchinski · 3 citations
Mathematics · Physics and Astronomy · #Bethe ansatz #Black Holes and Theoretical Physics #Conformal map #Coupling constant #Integrable system #Lambda #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear system #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Sigma #Sigma model #Superstring theory #Supersymmetry #Type (biology) #hep-th

paper · pdf · doi:10.1103/physrevd.72.086002

published as Phys.Rev.D72:086002,2005 · 30 pages, 1 figure, v2: references added

arxiv created 2005/09/09 · openalex publication_date 2005/10/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study an integrable conformal OSp(2m+2|2m) supercoset model as an analog to the AdS₅\ifmmode×\else\texttimes\fiS⁵ superstring world-sheet theory. Using the known S-matrix for this system, we obtain integral equations for states of large particle number in an SU(2) sector, which are exact in the sigma model coupling constant. As a check, we derive as a limit the general classical Bethe equation of Kazakov, Marshakov, Minahan, and Zarembo. There are two distinct quantum expansions around the well-studied classical limit, the \ensuremathλ^\ensuremath-1/2 effects and the 1/J effects. Our approach captures the first type, but not the second.

Citations

• Classical Non-Local conserved charges in String Theory
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Integrability of Three-Particle Evolution Equations in QCD
• A Novel Long Range Spin Chain and PlanarN=4 Super Yang-Mills
• High energy QCD as a completely integrable model
• Classical/quantum integrability in non-compact sector of AdS/CFT
• Aspects of semiclassical strings in AdS5
• Integrable Hamiltonian for Classical Strings on AdS5 × S5
• The algebraic curve of 1-loop planar N=4 SYM
• Linking Bäcklund and monodromy charges for strings on AdS5× S5
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Algebraic Curve for the SO(6) Sector of AdS/CFT
• The Dilatation Operator of \cal N = 4 SYM and Classical Limits of Spin Chains and Matrix Models
• Spin chain for quantum strings
• Semiclassical Bethe ansatz and AdS/CFT
• The dilatation operator of N=4 super Yang–Mills theory and integrability
• Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models
• Baecklund transformations, energy shift and the plane wave limit
• Semiclassical strings and AdS/CFT

Cited by

• Quantum Integrability for Three-Point Functions of Maximally Supersymmetric Yang-Mills Theory
• On AdS5×S5 string S-matrix
• Asymptotic Bethe ansatz from string sigma model on S3×R