Noncommutative Induced Gauge Theory

TL;DR

This paper derives a one-loop effective gauge action on 4D Moyal space, revealing additional terms akin to harmonic oscillator contributions that could lead to a renormalisable noncommutative gauge theory.

Contribution

It introduces a candidate for a renormalisable noncommutative gauge theory action, extending the understanding of gauge theories on Moyal space with new harmonic oscillator-like terms.

Findings

Effective action includes noncommutative Yang-Mills and additional harmonic oscillator terms.

Additional terms may ensure renormalisability of noncommutative gauge theories.

Proposes a candidate for a renormalisable gauge theory on Moyal space.

Abstract

We consider an external gauge potential minimally coupled to a renormalisable scalar theory on 4-dimensional Moyal space and compute in position space the one-loop Yang-Mills-type effective theory generated from the integration over the scalar field. We find that the gauge invariant effective action involves, beyond the expected noncommutative version of the pure Yang-Mills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic oscillator term, which for the noncommutative $\phi^4$-theory on Moyal space ensures renormalisability. The expression of a possible candidate for a renormalisable action for a gauge theory defined on Moyal space is conjectured and discussed.