Noncommutative gauge theories defined via Seiberg-Witten map have desirable properties that theories defined directly in terms of noncommutative fields lack, covariance and unrestricted choice of gauge group and charge being among them, but nonperturbative results in the deformation parameter θ are hard to obtain. In this article we use a θ-exact approach to study UV/IR mixing in a noncommutative quantum electrodynamics (NCQED) model defined via Seiberg-Witten map. The fermion contribution of the one loop correction to the photon propagator is computed and it is found that it gives the same UV/IR mixing term as a NCQED model without Seiberg-Witten map.

We study one-loop photon (Π) and neutrino (Σ) self-energies in a U(1) covariant gauge-theory on d-dimensional noncommutative spaces determined by a antisymmetricconstant tensor θ µν . For the general fermion-photon (S f ) and photon self-interaction (S g ) the closed form results reveal self-energies besetting with all kind of pathological terms: the UV divergence, the quadratic UV/IR mixing terms as well as a logarithmic IR divergent term of the type ln(µ 2 (θp) 2 ). In addition, the photon-loop produces new tensor structures satisfying transversality condition by themselves. We show that the photon self-energy in four-dimensional Euclidean spacetime can be reduced to two finite terms by imposing a specific full rank of θ µν and setting deformation parameters (κ f , κ g ) = (0, 3). In this case the neutrino two-point function vanishes. Thus for a specific point (0, 3) in the parameterspace (κ f , κ g ), a covariant θ-exact approach is able to produce a divergence-free result for one-loop quantum corrections, having also well-defined both the commutative limit as well as the pointlike limit of an extended object. While in two-dimensional space the photon self-energy is finite for arbitrary (κ f , κ g ) combinations, the neutrino self-energy still contains an superficial IR divergence.

One-loop theta-exact quantum corrections to the neutrino propagator are computed in noncommutative U*(1) gauge-theory based on Seiberg-Witten maps. Our closed form results show that the one-loop correction contains a hard 1/epsilon UV divergence, as well as a logarithmic IR-divergent term of the type ln sqrt(theta p)^2, thus considerably softening the usual UV/IR mixing phenomenon. We show that both of these problematic terms vanish for a certain choice of the noncommutative parameter theta which preserves unitarity. We find non-perturbative modifications of the neutrino dispersion relations which are assymptotically independent of the scale of noncommutativity in both the low and high energy limits and may allow superluminal propagation. Finally, we demonstrate how the prodigious freedom in Seiberg-Witten maps may be used to affect neutrino propagation in a profound way.Comment: 27 pages, 2 figures, Version to appear in JHE

In formulating gauge field theories on noncommutative (NC) spaces it is suggested that particles carrying gauge invariant quantities should not be viewed as pointlike, but rather as extended objects whose sizes grow linearly with their momenta. This and other generic properties deriving from the nonlocal character of interactions (showing thus unambiguously their quantum-gravity origin) lead to a specific form of UV/IR mixing as well as to a pathological behavior at the quantum level when the noncommutativity parameter theta is set to be arbitrarily small. In spite of previous suggestions that in a NC gauge theory based on the theta-expanded Seiberg-Witten (SW) maps UV/IR mixing effects may be under control, a fairly recent study of photon self-energy within a SW theta-exact approach has shown that UV/IR mixing is still present. We study the self-energy contribution for neutral fermions in the theta-exact approach of NC QED, and show by explicit calculation that all but one divergence can be eliminated for a generic choice of the noncommutativity parameter theta. The remaining divergence is linked to the pointlike limit of an extended object.Comment: 10 pages, a figure added, version to appear in JHE

We study two distinct θ-exact Seiberg-Witten (SW) map expansions, (I) and (II) respectively, up to e 3 order for the gauge parameter, gauge field and the gauge field strengths of the noncommutative U⋆(1) gauge theory on the Moyal space. We derive explicitly the closed form expression for the SW map ambiguity between the two and observe the emergence of several new totally commutative generalized star products. We also identify the additional gauge freedoms within each of the e 3 order field strength expansions and define corresponding sets of deformation/ratio/weight parameters, (κ, κi) and (κ, κ ′ i ), for these two SW maps respectively. 1 Generically the ordering employed in this article is the formal power of field operators or the homogeneity in the fields [23]. The equivalent notation of coupling constant ordering is a consequence of the so-called U⋆(1) charge quantization issue and its resolution within the SW map approach [5,27]. In this resolution [5,27] the commutative field in the SW map expansion for a U⋆(1) theory are bundled with the commutative charge Qe in order to normalize the NC field to the quantized charges 0, ±1, which in turn induces the equivalence between the field operator and coupling constant power ordering. We use the name coupling constant ordering for its easier visibility in (front of) the equations.