Scaling function in AdS/CFT from the O(6) sigma model

Abstract

Asymptotic behavior of the anomalous dimensions of Wilson operators with high spin and twist is governed in planar N=4 SYM theory by the scaling function which coincides at strong coupling with the energy density of a two-dimensional bosonic O(6) sigma model. We calculate this function by combining the two-loop correction to the energy density for the O(n) model with two-loop correction to the mass gap determined by the all-loop Bethe ansatz in N=4 SYM theory. The result is in agreement with the prediction coming from the thermodynamical limit of the quantum string Bethe ansatz equations, but disagrees with the two-loop stringy corrections to the folded spinning string solution.

25 pages, 2 figures

References in corpus (13)

• Comments on operators with large spin
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT
• The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
• A Generalized Scaling Function for AdS/CFT
• Strong-coupling expansion of cusp anomaly from quantum superstring
• 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
• Strong coupling for planar $\mathcal{N}=4$ SYM theory: an all-order result
• Nonperturbative scales in AdS/CFT
• Strong coupling expansion of Baxter equation in N=4 SYM
• The integrable O(6) model and the correspondence: checks and predictions

Cited by in corpus (5)

• Spinning strings at one-loop in AdS_4 x P^3
• Nonperturbative scales in AdS/CFT
• Bogoliubov compensation principle in the electro-weak interaction: value of the gauge constant, muon g-2 anomaly, predictions for Tevatron and LHC
• 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