Supersymmetry and the Yang-Mills Effective Action at Finite N

TL;DR

This paper investigates the supersymmetric structure of the effective action in SU(N) Yang-Mills theories, revealing non-renormalization properties of certain fermionic terms at specific loop orders and discussing their dependence on the gauge group rank.

Contribution

It demonstrates that specific fermionic terms in the effective action are one- or two-loop exact and introduces the concept of generalized F-terms for higher-order structures.

Findings

Eight fermion terms are one-loop exact.

Twelve fermion terms are two-loop exact for N=3.

Higher-order generalized F-terms may appear as the gauge group rank increases.

Abstract

We study the effective action of quantum mechanical SU(N) Yang-Mills theories with sixteen supersymmetries and N>2. We show that supersymmetry requires that the eight fermion terms in the supersymmetric completion of the $v^4$ terms be one-loop exact. We also show that the twelve fermion terms in the supersymmetric completion of the $v^6$ terms are two-loop exact for N=3. For N>3, this no longer seems to be true; we are able to find non-renormalization theorems for only certain twelve fermion structures. We call these structures `generalized F-terms.' We argue that as the rank of the gauge group is increased, there can be more generalized F-terms at higher orders in the derivative expansion.