Some Non-Renormalization Theorems for Higher Derivative Operators

TL;DR

This paper proves that certain four-derivative terms in the effective action of a supersymmetric matrix model are not renormalized, supporting its potential as a non-perturbative definition of M-theory.

Contribution

It provides a perturbative proof of non-renormalization theorems for higher derivative operators in a supersymmetric matrix model.

Findings

Four-derivative terms are not renormalized in the model.

Supports the model's role in non-perturbative M-theory.

Provides a perturbative validation of non-renormalization theorems.

Abstract

It has been argued that a certain large $N$ matrix model may provide a non-perturbative definition of $M$-theory. This model is the truncation to $0+1$ dimensions of ten-dimensional supersymmetric Yang-Mills theory. It is crucial to this identification that terms with four derivatives in the effective action for the quantum mechanics should not be renormalized. We offer a perturbative proof of this result.