Comments on Higher Derivative Operators in Some SUSY Field Theories

TL;DR

This paper investigates higher derivative operators in supersymmetric field theories, demonstrating their symmetry-determined nature, one-loop generation, and contrasting renormalization properties between four and three dimensions.

Contribution

It reveals that certain irrelevant operators in N=2 and N=4 supersymmetric theories are symmetry-determined, generated at one loop, and not renormalized beyond that in four dimensions.

Findings

Operators are symmetry-determined and generated at one loop.

Non-renormalization holds in four dimensions but not in three.

Instanton effects cause renormalization in three-dimensional theories.

Abstract

We study the leading irrelevant operators along the flat directions of certain supersymmetric theories. In particular, we focus on finite N=2 (including N=4) supersymmetric field theories in four dimensions and show that these operators are completely determined by the symmetries of the problem. This shows that they are generated only at one loop and are not renormalized beyond this order. An instanton computation in similar three dimensional theories shows that these terms are renormalized. Hence, the four dimensional non-renormalization theorem of these terms is not valid in three dimensions.