Wronskian solution for AdS/CFT Y-system

2010/10/31 by Nikolay Gromov, Vladimir Kazakov, Sébastien Leurent +2 · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Combinatorics #Generalization #Geometry #Homogeneous space #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Parameterized complexity #Physics #Planar #Pure mathematics #Quantum mechanics #Spectrum (functional analysis) #Wronskian #hep-th #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1007/jhep01(2011)155

published as JHEP 1101:155,2011 · 31 pages, 4 figures, 1 attached mathematica file

arxiv created 2010/11/26 · openalex publication_date 2011/01/01 · arxiv updated 2011/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Using the discrete Hirota integrability we find the general solution of the full quantum Y-system for the spectrum of anomalous dimensions of operators in the planar AdS 5 /CFT 4 correspondence in terms of Wronskian-like determinants parameterized by a finite number of Baxter’s Q-functions. We consider it as a useful step towards the construction of a finite system of non-linear integral equations (FiNLIE) for the full spectrum. The explicit asymptotic form of all the Q-functions for the large size operators is presented. We establish the symmetries and the analyticity properties of the asymptotic Q-functions and discuss their possible generalization to any finite size operators.

Citations

• Finite-size effects in the superconformal β-deformed 𝒩 = 4 SYM
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• A Novel Long Range Spin Chain and PlanarN=4 Super Yang-Mills
• Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra sl(r+1∣s+1)
• Classical/quantum integrability in non-compact sector of AdS/CFT
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• Y-system, TBA and Quasi-Classical Strings in AdS 4 × CP3
• Algebraic Curve for the SO(6) Sector of AdS/CFT
• Konishi operator at intermediate coupling
• TBA and Y-system for planar AdS4/CFT3
• Exact anomalous dimensions of N=4 Yang–Mills operators with large R charge

Cited by

• Wronskian solutions of the T-, Q- and Y-systems related to infinite dimensional unitarizable modules of the general linear superalgebra gl(M|N)