2009/11/30 by Gleb Arutyunov, Sergey Frolov, Ryo Suzuki · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Ansatz #Bethe ansatz #Dimension (graph theory) #Duality (order theory) #Excited state #Operator (biology) #Quantum Chromodynamics and Particle Interactions #Scaling #Scaling dimension #Spectral Theory in Mathematical Physics #String (physics) #hep-th
paper · pdf · doi:10.1007/jhep05(2010)031
published as JHEP 1005:031,2010 · 69 pages, v2: new "hybrid" equations for YQ-functions, figures and tables are added. Analyticity of Y-system is discussed, v3: published version
arxiv created 2010/04/12 · openalex publication_date 2010/05/01 · arxiv updated 2015/03/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We apply the contour deformation trick to the Thermodynamic Bethe Ansatz equations for the AdS5 × S5 mirror model, and obtain the integral equations determining the energy of two-particle excited states dual to N=4 SYM operators from the sl(2) sector. We show that each state/operator is described by its own set of TBA equations. Moreover, we provide evidence that for each state there are infinitely-many critical values of 't Hooft coupling constant λ, and the excited states integral equations have to be modified each time one crosses one of those. In particular, estimation based on the large L asymptotic solution gives λ≈ 774 for the first critical value corresponding to the Konishi operator. Our results indicate that the related calculations and conclusions of Gromov, Kazakov and Vieira should be interpreted with caution. The phenomenon we discuss might potentially explain the mismatch between their recent computation of the scaling dimension of the Konishi operator and the one done by Roiban and Tseytlin by using the string theory sigma model.