Functional BES equation

Abstract

We give a realization of the Beisert, Eden and Staudacher equation for the planar N=4 supersymetric gauge theory whichseems to be particularly useful to study the strong coupling limit. We use a linearized version of the BES equation as two coupled equations involving an auxiliary density function. We write these equations in terms of the resolvents and we transform them into to a system of functional, instead of integral, equations. We solve the functional equations perturbatively in the strong coupling limit and reproduce the recursive solution obtained by Basso, Korchemsky and Kotanski. The coefficients of the strong coupling expansion are fixed by the analyticity properties obeyed by the resolvents.

References added

References in corpus (19)

• Giant Magnons
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Quantum corrections to the string Bethe ansatz
• Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling
• Logarithmic scaling in gauge/string correspondence
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• On the highest transcendentality in N=4 SUSY
• On the Singularities of the Magnon S-matrix
• Two-loop world-sheet corrections in AdS_5 x S^5 superstring
• Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$
• Four-Loop Cusp Anomalous Dimension From Obstructions
• On the Strong Coupling Scaling Dimension of High Spin Operators
• The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
• A Generalized Scaling Function for AdS/CFT
• Strong coupling limit of Bethe Ansatz equations
• Spinning superstrings at two loops: strong-coupling corrections to dimensions of large-twist SYM operators
• The scaling function at strong coupling from the quantum string Bethe equations
• Strong coupling expansion of Baxter equation in N=4 SYM

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