Five-loop Konishi in N=4 SYM

TL;DR

The paper introduces a novel method for calculating the five-loop Konishi anomalous dimension in N=4 SYM, utilizing OPE analysis and dimensional regularization, avoiding traditional Feynman diagrams, and confirming results with integrability predictions.

Contribution

A new approach for computing Konishi anomalous dimension at five loops that simplifies calculations and extends beyond the planar limit using OPE and regularization techniques.

Findings

Analytic five-loop Konishi anomalous dimension obtained.

Results agree with integrability predictions in AdS/CFT.

Method reduces complex calculations to known integrals.

Abstract

We present a new method for computing the Konishi anomalous dimension in N=4 SYM at weak coupling. It does not rely on the conventional Feynman diagram technique and is not restricted to the planar limit. It is based on the OPE analysis of the four-point correlation function of stress-tensor multiplets, which has been recently constructed up to six loops. The Konishi operator gives the leading contribution to the singlet SU(4) channel of this OPE. Its anomalous dimension is the coefficient of the leading single logarithmic singularity of the logarithm of the correlation function in the double short-distance limit, in which the operator positions coincide pairwise. We regularize the logarithm of the correlation function in this singular limit by a version of dimensional regularization. At any loop level, the resulting singularity is a simple pole whose residue is determined by a finite two-point integral with one loop less. This drastically simplifies the five-loop calculation of the Konishi anomalous dimension by reducing it to a set of known four-loop two-point integrals and two unknown integrals which we evaluate analytically. We obtain an analytic result at five loops in the planar limit and observe perfect agreement with the prediction based on integrability in AdS/CFT.