Non-Renormalization Theorems for Operators with Arbitrary Numbers of Derivatives in ${\cal N}=4$ Yang Mills Theory

TL;DR

This paper extends non-renormalization theorems in supersymmetric Yang-Mills theories, showing that certain derivative operators are exactly determined and not renormalized, with implications for understanding quantum corrections in these theories.

Contribution

It generalizes non-renormalization proofs to operators with arbitrary derivatives in ${ m SU}(N)$ gauge theories, including finite ${ m N}=2$ cases.

Findings

Operators with 2N derivatives are not renormalized in ${ m SU}(N)$ theories.

Such operators can be exactly computed through simple perturbative methods.

Results have implications for the structure of quantum corrections in supersymmetric gauge theories.

Abstract

We generalize the proof of the non-renormalization of the four derivative operators in ${\cal N}=4$ Yang Mills theory with gauge group SU(2) to show that certain terms with 2N derivatives are not renormalized in the theory with gauge group SU(N). These terms may be determined exactly by a simple perturbative computation. Similar results hold for finite ${\cal N}=2$ theories. We comment on the implications of these results.