Vanishing of the four-loop charge renormalization function in N=4 SYM theory

TL;DR

This paper computes the four-loop renormalization constants in N=4 supersymmetric Yang-Mills theory, confirming the vanishing of the beta-function, which supports the theory's conformal invariance at this order.

Contribution

It provides a four-loop calculation of renormalization constants in N=4 SYM, demonstrating the beta-function remains zero, thus extending previous lower-order results.

Findings

Beta-function is zero at four loops from gauge and Yukawa vertices.

Supports the conformal invariance of N=4 SYM at higher loops.

Provides detailed four-loop renormalization constants.

Abstract

We calculate the renormalization constants of the maximally extended N=4 supersymmetric Yang-Mills theories in the dimensional reduction scheme up to four loops. We have found, that the beta-function is zero both from gauge and Yukawa vertices.