On Matrix Model Formulations of Noncommutative Yang-Mills Theories

TL;DR

This paper investigates the stability of noncommutative spaces in matrix models and finds that bosonic models are generally unstable, while supersymmetric models with specific deformations can maintain stability, impacting the formulation of noncommutative Yang-Mills theories.

Contribution

It demonstrates the instability of noncommutative spaces in bosonic matrix models and shows stability in a supersymmetric deformed model, clarifying conditions for well-defined noncommutative Yang-Mills theories.

Findings

Bosonic noncommutative spaces are unstable.

Supersymmetric deformed models can stabilize noncommutative backgrounds.

Perturbative instability persists nonperturbatively in bosonic models.

Abstract

We study stability of noncommutative spaces in matrix models and discuss the continuum limit which leads to noncommutative Yang-Mills theories (NCYM). It turns out that most of noncommutative spaces in bosonic models are unstable. This indicates perturbative instability of fuzzy R^D pointed out by Van Raamsdonk and Armoni et al. persists to nonperturbative level in these cases. In this sense, these bosonic NCYM are not well-defined, or at least their matrix model formulations studied in this paper do not work. We also show that noncommutative backgrounds are stable in a supersymmetric matrix model deformed by a cubic Myers term, though the deformation itself breaks supersymmetry.