Fusion hierarchies for N = 4 superYang-Mills theory

Abstract

We employ the analytic Bethe Anzats to construct eigenvalues of transfer matrices with finite-dimensional atypical representations in the auxiliary space for the putative long-range spin chain encoding anomalous dimensions of all composite single-trace gauge invariant operators of the maximally supersymmetric Yang-Mills theory. They obey an infinite fusion hierarchy which can be reduced to a finite set of integral relations for a minimal set of transfer matrices. This set is used to derive a finite systems of functional equations for eigenvalues of nested Baxter polynomials.

arXiv comment24 pages, 2 figures

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• T-systems and Y-systems in integrable systems
• The S-matrix of String Bound States
• Solutions of the T-system and Baxter equations for supersymmetric spin chains
• Fine structure of anomalous dimensions in N=4 super Yang-Mills theory
• Luescher formula for GKP string
• Reciprocity of gauge operators in N=4 SYM
• QCD properties of twist operators in the N=6 Chern-Simons theory
• Nonlinear integrable couplings of a generalized super Ablowitz-Kaup-Newell-Segur hierarchy and its super bi-Hamiltonian structures
• Generalized Gribov-Lipatov Reciprocity and AdS/CFT
• Reciprocity and integrability in the sl(2) sector of N=4 SYM
• Unified approach to the SU(2) Principal Chiral Field model at Finite Volume
• QCD-like properties for anomalous dimensions in N=4 SYM