Strong coupling limit of Bethe Ansatz equations

Abstract

We develop a method to analyze the strong coupling limit of the Bethe ansatz equations supposed to give the spectrum of anomalous dimensions of the planar $\mathcal{N}=4$ gauge theory. This method is particularly adapted for the three rank-one sectors, $su(2)$, $su(1|1)$ and $sl(2)$. We use the elliptic parametrization of the Bethe ansatz variables, which degenerates to a hyperbolic one in the strong coupling limit. We analyze the equations for the highest excited states in the su(2) and $su(1|1)$ sectors and for the state corresponding to the twist-two operator in the $sl(2)$ sector, both without and with the dressing kernel. In some cases we were able to give analytic expressions for the leading order magnon densities. Our method reproduces all existing analytical and numerical results for these states at the leading order.

Typos corrected, references added, discrepancy with Beccaria at al. eliminated

References in corpus (47)

• Gauge Theory Correlators from Non-Critical String Theory
• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• The Bethe-Ansatz for N=4 Super Yang-Mills
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• A semi-classical limit of the gauge/string correspondence
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Transcendentality and Crossing
• The N=4 SYM Integrable Super Spin Chain
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Bethe Ansatz for Quantum Strings
• How Algebraic Bethe Ansatz works for integrable model
• Giant Magnons
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang-Mills model
• A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills
• The Factorized S-Matrix of CFT/AdS
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
• A Crossing-Symmetric Phase for AdS_5 x S^5 Strings
• Finite-size Effects from Giant Magnons
• Quantum corrections to the string Bethe ansatz
• Planar N=4 gauge theory and the Inozemtsev long range spin chain
• The Analytic Bethe Ansatz for a Chain with Centrally Extended su(2|2) Symmetry
• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• On AdS_5 x S^5 String S-matrix
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• Magnon Bound States and the AdS/CFT Correspondence
• Planar N=4 Gauge Theory and the Hubbard Model
• On the highest transcendentality in N=4 SUSY
• On the Singularities of the Magnon S-matrix
• Uniform Light-Cone Gauge for Strings in AdS_5 x S^5: Solving su(1|1) Sector
• Four-Loop Cusp Anomalous Dimension From Obstructions
• Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$
• On the Strong Coupling Scaling Dimension of High Spin Operators
• Quasiclassical QCD Pomeron
• Asymptotic Bethe Ansatz from String Sigma Model on S^3 x R
• Integrable Heisenberg-van Vleck chains with variable range exchange
• On the finite size corrections of anti-ferromagnetic anomalous dimensions in $\mathcal{N}=4$ SYM
• Hubbard's Adventures in $\mathcal{N}=4$ SYM-land? Some non-perturbative considerations on finite length operators
• Antiferromagnetic Operators in N=4 Supersymmetric Yang-Mills Theory
• The SU(2) sector in AdS/CFT
• On the Scattering of Magnon Boundstates
• On highest-energy state in the su(1|1) sector of N=4 super Yang-Mills theory
• Bethe Ansatz solutions for highest states in $\mathcal{N}=4$ SYM and AdS/CFT duality
• Highest states in light-cone $Ad{S}_5\times S^5$ superstring

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• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• On String S-matrix, Bound States and TBA
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• Two-loop world-sheet corrections in AdS_5 x S^5 superstring
• Wrapping interactions at strong coupling -- the giant magnon
• Semiclassical Quantization of Spinning Strings in AdS_4 x CP^3
• Exciting the GKP string at any coupling
• A Generalized Scaling Function for AdS/CFT
• Quantum folded string and integrability: from finite size effects to Konishi dimension
• q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit
• The Dressing Factor and Crossing Equations
• Spinning superstrings at two loops: strong-coupling corrections to dimensions of large-twist SYM operators
• Comment on the Scaling Function in AdS4 x CP3
• Functional BES equation
• Embedding nonlinear O(6) sigma model into N=4 super-Yang-Mills theory
• Scaling function in AdS/CFT from the O(6) sigma model
• Quantum integrability and functional equations
• The scaling function at strong coupling from the quantum string Bethe equations
• Review of AdS/CFT Integrability, Chapter III.3: The dressing factor
• Resurgence of the Cusp Anomalous Dimension
• On Symmetry Enhancement in the psu(1,1|2) Sector of N=4 SYM
• Fine structure of anomalous dimensions in N=4 super Yang-Mills theory
• The Resurgence of the Cusp Anomalous Dimension
• Generalized scaling function from light-cone gauge AdS_5 x S^5 superstring
• Nonperturbative scales in AdS/CFT
• q-Deformed Supersymmetry and Dynamic Magnon Representations
• Luescher formula for GKP string
• Quark scattering amplitudes at strong coupling
• Factorized world-sheet scattering in near-flat AdS_5 x S^5
• Reciprocity of gauge operators in N=4 SYM
• Minimal solution of the AdS/CFT crossing equation
• Strong coupling expansion of Baxter equation in N=4 SYM
• The generalised scaling function: a systematic study
• Algebraic Curves for Long Folded and Circular Winding Strings in AdS5xS5
• Review of AdS/CFT Integrability, Chapter III.4: Twist states and the cusp anomalous dimension
• Towards NMHV amplitudes at strong coupling
• On the high spin expansion in the $sl(2)$ $\mathcal{N}=4$ SYM theory
• On the logarithmic powers of $sl(2)$ SYM${}_4$
• Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs
• TBA-like equations and Casimir effect in (non-)perturbative AdS/CFT
• From nesting to dressing
• The high spin expansion of twist sector dimensions: the planar N=4 super Yang-Mills theory
• Microscopic formulation of the S-matrix in AdS/CFT
• The Ising model and planar N=4 Yang-Mills
• On the dressing phase in the SL(2) Bethe Ansatz
• DGLAP and BFKL equations in $\mathcal{N}=4$ SYM: from weak to strong coupling
• Gauge-String Dualities and Some Applications
• Spiky Strings with Two Spins in AdS5