On the high spin expansion in the $sl(2)$ $\mathcal{N}=4$ SYM theory

Abstract

We study the the high spin expansion of the anomalous dimension for long operators belonging to the $sl(2)$ sector of $\mathcal{N}=4$ SYM. Keeping the ratio $j$ between the twist and the logarithm of the spin fixed, the anomalous dimensions expand as $\gamma =f(g,j)\ln s+f^{(0)}(g,j)+O(1/\ln s)$. This particular double scaling limit is efficiently described, up to the desired accuracy $O(\ln s^0)$, in terms of linear integral equations. By using them, we are able to evaluate both at weak and strong coupling the sub-leading scaling function $f^{(0)}(g,j)$ as series in $j$, up to the order $j^5$. Thanks to these results, the possible extension of the liaison with the O(6) non-linear sigma model may be tackled on a solid ground.

References in corpus (44)

• Gauge Theory Correlators from Non-Critical String Theory
• The Bethe-Ansatz for N=4 Super Yang-Mills
• Transcendentality and Crossing
• The N=4 SYM Integrable Super Spin Chain
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Bethe Ansatz for Quantum Strings
• The Factorized S-Matrix of CFT/AdS
• Comments on operators with large spin
• Baryon Distribution Amplitudes in QCD
• Integrability of three-particle evolution equations in QCD
• Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling
• Excited State Destri - De Vega Equation for Sine-Gordon and Restricted Sine-Gordon Models
• Logarithmic scaling in gauge/string correspondence
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• Four loop twist two, BFKL, wrapping and strings
• Anomalous dimensions of high-spin operators beyond the leading order
• On the highest transcendentality in N=4 SUSY
• Renormalization of twist-three operators and integrable lattice models
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT
• Non linear integral equation and excited--states scaling functions in the sine-Gordon model
• Fine structure of spectrum of twist-three operators in QCD
• 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
• N=4 SUSY Yang--Mills: three loops made simple(r)
• Strong coupling limit of Bethe Ansatz equations
• Spinning superstrings at two loops: strong-coupling corrections to dimensions of large-twist SYM operators
• Embedding nonlinear O(6) sigma model into N=4 super-Yang-Mills theory
• Functional BES equation
• Structure of large spin expansion of anomalous dimensions at strong coupling
• Large spin corrections in $\mathcal{N}=4$ SYM sl(2): still a linear integral equation
• Scaling function in AdS/CFT from the O(6) sigma model
• The scaling function at strong coupling from the quantum string Bethe equations
• Strong coupling for planar $\mathcal{N}=4$ SYM theory: an all-order result
• Fine structure of anomalous dimensions in N=4 super Yang-Mills theory
• The virtual scaling function of AdS/CFT
• Beyond cusp anomalous dimension from integrability
• Generalized Scaling Function at Strong Coupling
• The generalised scaling function: a note
• The generalised scaling function: a systematic study
• The 2-loop generalized scaling function from the BES/FRS equation
• The integrable O(6) model and the correspondence: checks and predictions
• Thermostatistics of a single particle on a granular dimer lattice: influence of defects
• The generalized scaling function of AdS/CFT and semiclassical string theory

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• Spiky strings in the SL(2) Bethe Ansatz
• On the logarithmic powers of $sl(2)$ SYM${}_4$
• TBA-like equations and Casimir effect in (non-)perturbative AdS/CFT
• Reciprocity and integrability in the sl(2) sector of N=4 SYM
• The high spin expansion of twist sector dimensions: the planar N=4 super Yang-Mills theory
• Generalised scaling at subleading order
• Operator with large spin and spinning D3-brane
• Beyond cusp anomalous dimension from integrability in SYM${}_4$