The generalised scaling function: a note

Abstract

A method for determining the generalised scaling function(s) arising in the high spin behaviour of long operator anomalous dimensions in the planar $sl(2)$ sector of $\mathcal{N}=4$ SYM is proposed. The all-order perturbative expansion around the strong coupling is detailed for the prototypical third and fourth scaling functions, showing the emergence of the O(6) Non-Linear Sigma Model mass-gap from different SYM 'mass' functions. Remarkably, only the fourth one gains contribution from the non-BES reducible densities and also shows up, as first, NLSM interaction and specific model dependence. Finally, the computation of the $n$-th generalised function is sketched and might be easily finalised for checks versus the computations in the sigma model or the complete string theory.

Latex version, typos corrected, references and clarifications added

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• Fine structure of anomalous dimensions in N=4 super Yang-Mills theory
• Beyond cusp anomalous dimension from integrability
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• On wrapping corrections to GKP-like operators
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• The 2-loop generalized scaling function from the BES/FRS equation
• The integrable O(6) model and the correspondence: checks and predictions
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• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes II: Young tableaux, asymptotic factorisation and strong coupling
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• Generalised scaling at subleading order
• Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory
• Exact results for the low energy AdS(4)XCP(3) string theory