Comments on operators with large spin

TL;DR

This paper analyzes high spin operators in gauge theories, revealing their anomalous dimensions' logarithmic scaling, the origin of divergences, and connections to sigma models, with implications for string theory computations.

Contribution

It provides a symmetry-based argument for the logarithmic scaling of anomalous dimensions and links high spin operators to bosonic sigma models in a specific limit.

Findings

Logarithmic scaling of anomalous dimensions for high spin operators

Origin of double logarithmic divergence in the Sudakov factor

Connection between cusp anomalous dimension and energy density in AdS/CFT

Abstract

We consider high spin operators. We give a general argument for the logarithmic scaling of their anomalous dimensions which is based on the symmetries of the problem. By an analytic continuation we can also see the origin of the double logarithmic divergence in the Sudakov factor. We show that the cusp anomalous dimension is the energy density for a flux configuration of the gauge theory on $AdS_3 \times S^1$. We then focus on operators in ${\cal N}=4$ super Yang Mills which carry large spin and SO(6) charge and show that in a particular limit their properties are described in terms of a bosonic O(6) sigma model. This can be used to make certain all loop computations in the string theory.