Noncommutative field theories with harmonic term

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.