Noncommutative field theories with harmonic term

TL;DR

This paper discusses how adding a harmonic term to noncommutative scalar and gauge field theories on Moyal space removes UV-IR mixing, making them renormalizable, and explores their supergeometric interpretation and duality properties.

Contribution

It introduces the supergeometric interpretation of the harmonic term and its role in achieving renormalizability in noncommutative field theories.

Findings

Harmonic term removes UV-IR mixing in scalar theory

Scalar and gauge models exhibit duality related to Langmann-Szabo symmetry

Potential renormalizability of the gauge theory is discussed

Abstract

The UV-IR mixing of scalar field theory on the Moyal space is removed by the harmonic term, so that the theory is renormalizable. We will present different properties of this scalar model and its associated gauge theory, which is candidate to renormalizability. The supergeometric interpretation of the harmonic term, for both scalar and gauge models, and related to the Langmann-Szabo duality, will be exposed.