Three loop anomalous dimensions of twist-3 gauge operators in N=4 SYM

TL;DR

This paper derives a closed-form expression for the three-loop anomalous dimensions of certain twist-3 gauge operators in N=4 SYM, using Bethe Ansatz equations and principles of transcendentality and reciprocity.

Contribution

It provides the first analytical formula for three-loop anomalous dimensions of twist-3 operators in N=4 SYM, extending previous one-loop results.

Findings

The formula reproduces the universal cusp anomalous dimension.

It obeys recursion relations based on reciprocity invariance.

The approach involves solving Bethe Ansatz equations at finite spin.

Abstract

We propose a closed expression for the three loop anomalous dimension of a class of twist-3 operators built with gauge fields and covariant derivatives. To this aim, we solve the long-range Bethe Ansatz equations at finite spin and provide a consistent analytical formula obtained assuming maximal transcendentality violation as suggested by the known one-loop anomalous dimension. The final result reproduces the universal cusp anomalous dimension and obeys recursion relations inspired by the principle of reciprocity invariance.