One Loop Renormalizability of Supersymmetric Yang-Mills Theories on Noncommutative Two-Torus

TL;DR

This paper demonstrates that noncommutative Yang-Mills theories on a two-torus are one-loop renormalizable by relating them to gauge theories in commutative space, analyzing UV/IR limits and moduli space.

Contribution

It establishes the one-loop renormalizability of noncommutative Yang-Mills theories on a two-torus through a novel gauge theory formulation.

Findings

The theory is one-loop renormalizable in the continuum limit.

The gauge group generalizes area-preserving diffeomorphisms to noncommutative space.

Discussion of UV/IR limits and vacua moduli space.

Abstract

We argue that Yang-Mills theory on noncommutative torus, expressed in the Fourrier modes, is described by a gauge theory in a usual commutative space, the gauge group being a generalization of the area-preserving diffeomorphisms to the noncommutative case. In this way, performing the loop calculation in this gauge theory in the continuum limit we show that this theory is {\it one loop renormalizable}, and discuss the UV and IR limits. The moduli space of the vacua of the noncommutative super Yang-Mills theories in (2+1) dimensions is discussed.