When considering quantum field theories on non-commutative spaces one inevitably encounters the infamous UV/IR mixing problem. So far, only very few renormalizable models exist and all of them describe non-commutative scalar field theories on fourdimensional Euclidean Groenewold-Moyal deformed space, also known as 'θ-deformed space' R 4 θ . In this work we discuss some major obstacles of constructing a renormalizable non-commutative gauge field model and sketch some possible ways out.

In this paper we discuss one-loop results for the translation invariant non-commutative gauge field model we recently introduced in ref. [1]. This model relies on the addition of some carefully chosen extra terms in the action which mix long and short scales in order to circumvent the infamous UV/IR mixing, and were motivated by the renormalizable non-commutative scalar model of Gurau et al. [2].

Based on our recent findings regarding (non-)renormalizability of non-commutative U⋆(1) gauge theories [1, 2] we present the construction of a new type of model. By introducing a soft-breaking term in such a way that only the bilinear part of the action is modified, no interaction between the gauge sector and auxiliary fields occurs. Demanding in addition that the latter form BRST doublet structures, this leads to a minimally altered non-commutative U⋆(1) gauge model featuring an IR damping behavior. Moreover, the new breaking term is shown to provide the necessary structure in order to absorb the inevitable quadratic IR divergences appearing at one-loop level in theories of this kind. In this paper we compute Feynman rules, symmetries and results for the vacuum polarization together with the one-loop renormalization of the gauge boson propagator and three-point functions.

Motivated by the recent work of Vilar et al.[1] we enhance our non-commutative translation invariant gauge model [2] by introducing auxiliary fields and ghosts forming a BRST doublet structure. In this way localization of the problematic 1 D 2 term can be achieved without the necessity for any additional degrees of freedom. The resulting theory is suspected to be renormalizable. A rigorous proof, however, has not been accomplished up to now.

Abstract. This paper carries forward a series of articles describing our enterprise to construct a gauge equivalent for the θ-deformed non-commutative The reason is that this dimensionless operator is invariant with respect to any symmetry of the model, and can be inserted to arbitrary power. In the present article we discuss explicit one-loop calculations, and analyze the mechanism the mentioned problems originate from.