Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings

2005/04/30 by Niklas Beisert, Matthias Staudacher · 87 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2005.06.038

published as Nucl.Phys.B727:1-62,2005 · 67 pages, In Honor of Hans Bethe, v2: references added, typos fixed, sign conventions improved, v3: published version

openalex publication_date 2005/08/26 · arxiv created 2005/09/26 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

We generalize various existing higher-loop Bethe ansaetze for simple sectors of the integrable long-range dynamic spin chain describing planar N=4 Super Yang-Mills Theory to the full psu(2,2|4) symmetry and, asymptotically, to arbitrary loop order. We perform a large number of tests of our conjectured equations, such as internal consistency, comparison to direct three-loop diagonalization and expected thermodynamic behavior. In the special case of the su(1|2) subsector, corresponding to a long-range t-J model, we are able to derive, up to three loops, the S-matrix and the associated nested Bethe ansatz from the gauge theory dilatation operator. We conjecture novel all-order S-matrices for the su(1|2) and su(1,1|2) subsectors, and show that they satisfy the Yang-Baxter equation. Throughout the paper, we muse about the idea that quantum string theory on AdS₅xS⁵ is also described by a psu(2,2|4) spin chain. We propose asymptotic all-order Bethe equations for this putative "string chain", which differ in a systematic fashion from the gauge theory equations.

Citations

• A New Solution of the Supersymmetric TJ Model by Means of the Quantum Inverse Scattering Method
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory

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