A Generalized Scaling Function for AdS/CFT

TL;DR

The paper investigates a refined large-spin limit for sl(2) twist operators in planar N=4 SYM, proposing a two-parameter generalized scaling function f(g,j) that potentially bridges weak-gauge theory and strong-string theory regimes. It derives a non-perturbative integral equation (an NLIE with hole contributions and a gap parameter a) governing f(g,j) and demonstrates a weak-coupling double expansion, including the notable result that the quadratic j-term f2(g) vanishes. The work generalizes the known BES/ES-type kernels to this refined limit and provides explicit expressions for the leading and subleading behavior of the scaling function, highlighting bi-analyticity in g and j and laying groundwork for strong-coupling extrapolation. Overall, it offers a controlled, integrability-based framework to interpolate between gauge-theory and string-theory observables within the AdS/CFT correspondence, with clear predictions for the hole contributions and corrections to twist-operator dimensions.

Abstract

We study a refined large spin limit for twist operators in the sl(2) sector of AdS/CFT. We derive a novel non-perturbative equation for the generalized two-parameter scaling function associated to this limit, and analyze it at weak coupling. It is expected to smoothly interpolate between weakly coupled gauge theory and string theory at strong coupling.