Anomalous dimensions of finite size field strength operators in N=4 SYM

TL;DR

This paper derives compact formulas for the anomalous dimensions of certain gluonic operators in N=4 SYM, matching Bethe Ansatz predictions up to five loops and revealing potential hidden relations.

Contribution

It introduces closed-form expressions for anomalous dimensions of operators in N=4 SYM that align with Bethe Ansatz results and uncover size-dependent patterns.

Findings

Formulas match Bethe Ansatz predictions up to five loops

Size dependence shows a simple, predictable pattern

Reveals potential hidden relations among operators

Abstract

In the N=4 super Yang-Mills theory, we consider the higher order anomalous dimensions gamma_L(g) of purely gluonic operators Tr(F^L) where F is a component of the self-dual field strength. We propose compact closed expressions depending parametrically on L that reproduce the prediction of Bethe Ansatz equations up to five loop order, including transcendental dressing corrections. The size dependence follows a simple pattern as the perturbative order is increased and suggests hidden relations for these special operators.