Comments on operators with large spin

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.