The generalised scaling function: a systematic study

Abstract

We describe a procedure for determining the generalised scaling functions $f_n(g)$ at all the values of the coupling constant. These functions describe the high spin contribution to the anomalous dimension of large twist operators (in the $sl(2)$ sector) of $\mathcal{N}=4$ SYM. At fixed $n$, $f_n(g)$ can be obtained by solving a linear integral equation (or, equivalently, a linear system with an infinite number of equations), whose inhomogeneous term only depends on the solutions at smaller $n$. In other words, the solution can be written in a recursive form and then explicitly worked out in the strong coupling regime. In this regime, we also emphasise the peculiar convergence of different quantities ('masses', related to the $f_n(g)$) to the unique mass gap of the $O(6)$ nonlinear sigma model and analyse the first next-to-leading order corrections.

Latex version, journal version (with explanatory appendices and more references)

References in corpus (38)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Transcendentality and Crossing
• Superconformal Chern-Simons Theories and AdS_4/CFT_3 Correspondence
• Comments on operators with large spin
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• Superstrings on AdS_4 x CP^3 as a Coset Sigma-model
• The Bethe ansatz for superconformal Chern-Simons
• The SU(2) x SU(2) sector in the string dual of N=6 superconformal Chern-Simons theory
• The all loop AdS4/CFT3 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
• N=6 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT
• Semiclassical Quantization of Spinning Strings in AdS_4 x CP^3
• Spinning strings at one-loop in AdS_4 x P^3
• Integrable Spin Chain in Superconformal Chern-Simons Theory
• 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
• Finite-size corrections in the SU(2) x SU(2) sector of type IIA string theory on AdS_4 x CP^3
• AdS4/CFT3 at One Loop
• Strong coupling limit of Bethe Ansatz 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
• Embedding nonlinear O(6) sigma model into N=4 super-Yang-Mills theory
• Functional BES equation
• Large spin corrections in $\mathcal{N}=4$ SYM sl(2): still a linear integral equation
• 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
• Generalized Scaling Function at Strong Coupling
• Hubbard's Adventures in $\mathcal{N}=4$ SYM-land? Some non-perturbative considerations on finite length operators
• The generalised scaling function: a note
• Strong coupling expansion of Baxter equation in N=4 SYM
• On the commuting charges for the highest dimension SU(2) operators in planar $\mathcal{N}=4$ SYM
• The integrable O(6) model and the correspondence: checks and predictions
• The generalized scaling function of AdS/CFT and semiclassical string theory

Cited by in corpus (16)

• Four loop twist two, BFKL, wrapping and strings
• Quantum integrability and functional equations
• Scaling function in AdS/CFT from the O(6) sigma model
• Review of AdS/CFT Integrability, Chapter III.3: The dressing factor
• Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: scattering, particles and minimal area Wilson loops
• Resurgence of the Cusp Anomalous Dimension
• Generalized scaling function from light-cone gauge AdS_5 x S^5 superstring
• Beyond cusp anomalous dimension from integrability
• Nonperturbative scales in AdS/CFT
• On wrapping corrections to GKP-like operators
• The 2-loop generalized scaling function from the BES/FRS equation
• On the high spin expansion in the $sl(2)$ $\mathcal{N}=4$ SYM theory
• On the logarithmic powers of $sl(2)$ SYM${}_4$
• TBA-like equations and Casimir effect in (non-)perturbative AdS/CFT
• QCD-like properties for anomalous dimensions in N=4 SYM
• Exact results for the low energy AdS(4)XCP(3) string theory