N=4 Super Yang-Mills Low-Energy Effective Action at Three and Four Loops

TL;DR

This paper proves that in N=4 super Yang-Mills theory, there are no three- and four-loop corrections to the low-energy effective action, highlighting a special non-renormalization property of the theory.

Contribution

The authors demonstrate the absence of three- and four-loop corrections to the non-holomorphic effective potential using harmonic superspace techniques.

Findings

No three-loop corrections to the effective potential.

No four-loop corrections to the effective potential.

Discussion of the mechanism behind the vanishing loop corrections.

Abstract

We investigate the low-energy effective action in N=4 super Yang-Mills theory with gauge group SU(n) spontaneously broken down to its maximal torus. Using harmonic superspace technique we prove an absence of any three- and four-loop corrections to non-holomorphic effective potential depending on N=2 superfield strengths. A mechanism responsible for vanishing arbitrary loop corrections to low-energy effective action is discussed.