Konishi Form Factor at Three Loop in ${\cal N}=4$ SYM

TL;DR

This paper computes third-order corrections to the Konishi operator's form factor in ${ m extbf{N}=4}$ SYM, revealing universal IR behavior and confirming UV anomalous dimensions, using Feynman diagrams in the $ar{DR}$ scheme.

Contribution

First third-order calculation of the Konishi form factor in ${ m extbf{N}=4}$ SYM, analyzing scheme dependence and IR/UV structures with novel insights into transcendental terms.

Findings

Third-order corrections satisfy the KG equation in $ar{DR}$ scheme.

IR anomalous dimensions match those of half-BPS operators.

Highest transcendental terms are identical to half-BPS operator.

Abstract

We present the first results on the third order corrections to on-shell form factor (FF) of the Konishi operator in ${\cal N}=4$ supersymmetric Yang-Mills theory using Feynman diagrammatic approach in modified dimensional reduction ($\overline {DR}$) scheme. We show that it satisfies KG equation in $\overline {DR}$ scheme while the result obtained in four dimensional helicity (FDH) scheme needs to be suitably modified not only to satisfy the KG equation but also to get the correct ultraviolet (UV) anomalous dimensions. We find that the cusp, soft and collinear anomalous dimensions obtained to third order are same as those of the FF of the half-BPS operator confirming the universality of the infrared (IR) structures of on-shell form factors. In addition, the highest transcendental terms of the FF of Konishi operator are identical to those of half-BPS operator indicating the probable existence of deeper structure of the on-shell FF. We also confirm the UV anomalous dimensions of Konishi operator up to third order providing a consistency check on the both UV and universal IR structures in ${\cal N}=4$.