Relation between gauge theories on R^3_λ and Group Field Theory

Determine whether the gauge theories formulated on the noncommutative space R^3_λ—constructed via the derivation-based differential calculus with inner derivations, covariant coordinates Φ_μ, and gauge-fixed actions such as S^f_Ω(Φ)—are actually related to specific Group Field Theory models in the sense of matching their noncommutative or matrix-model representations.

Background

The paper presents gauge theories on the noncommutative deformation R^3_λ described as an infinite direct sum of fuzzy spheres with inner derivation-based differential calculus. Using covariant coordinates, the authors construct gauge-invariant matrix models that include harmonic terms and show finiteness to all orders; one case is exactly solvable.

Given similarities with noncommutative and matrix-model formulations used in Group Field Theory, the authors highlight a possible connection but explicitly state that it is unknown whether the presented gauge theories correspond to particular Group Field Theory models.