On the Hierarchy Between Non-Commutative and Ordinary Supersymmetric Yang-Mills

TL;DR

This paper explores the relationship between non-commutative and ordinary supersymmetric Yang-Mills theories, proposing a hierarchy where the former dominates in the infrared and the latter in the ultraviolet, revealing a layered duality structure.

Contribution

It introduces a hierarchy between non-commutative and ordinary supersymmetric Yang-Mills theories, clarifying their domain-specific applicability and duality structure.

Findings

Non-commutative SYM with rational Theta is dual to ordinary SYM with 't Hooft flux.

The ordinary SYM describes the UV regime, while the non-commutative version describes the IR regime.

The two descriptions form a hierarchy, not a simple duality.

Abstract

Non-commutative supersymmetric Yang-Mills with rational Theta is dual to an ordinary supersymmetric Yang-Mills with a 't Hooft flux. It is believed that the simplest description is via the ordinary supersymmetric Yang-Mills. We claim, however, that the two descriptions form a hierarchy. The SYM description is the proper description in the ultra violet while the non-commutative description takes over in the infra red.