Supersymmetry and Higher Derivative Terms in the Effective Action of Yang-Mills Theories

TL;DR

This paper demonstrates how supersymmetry constraints precisely determine higher derivative terms, including their coefficients, in the effective action of certain Yang-Mills theories, especially in quantum mechanical gauge theories.

Contribution

It shows that requiring sixteen supersymmetries uniquely fixes the $v^6$ term and its coefficient in the effective action of quantum mechanical Yang-Mills theories.

Findings

The $v^6$ term is uniquely determined by supersymmetry.

The numerical coefficient of the $v^6$ term is fixed by lower derivative terms.

Supersymmetry imposes strong constraints on higher derivative terms in the effective action.

Abstract

Higher derivative terms in the effective action of certain Yang-Mills theories can be severely constrained by supersymmetry. We show that requiring sixteen supersymmetries in quantum mechanical gauge theory determines the $v^6$ term in the effective action. Even the numerical coefficient of the $v^6$ term is fixed in terms of lower derivative terms in the effective action.