Finite-size effect for four-loop Konishi of the beta-deformed N=4 SYM

TL;DR

This paper calculates the four-loop anomalous dimension of the Konishi operator in a beta-deformed N=4 SYM theory using twisted S-matrix elements, confirming the integrability-based predictions with perturbative gauge theory results.

Contribution

It introduces a novel approach using twisted S-matrix elements to describe the beta-deformation and computes the four-loop Konishi anomalous dimension, matching gauge theory calculations.

Findings

Exact agreement with perturbative gauge theory results

Validates the twisted S-matrix approach for deformed theories

Demonstrates the applicability of Luscher formula at four loops

Abstract

We propose that certain twists of the su(2|2) S-matrix elements describe the beta-deformation of N=4 supersymmetric Yang-Mills theory. We compute the perturbative four-loop anomalous dimension of the Konishi operator of the deformed gauge theory from the Luscher formula based on these twisted S-matrix elements. The result agrees exactly with the perturbative gauge theory computations.