Wilson lines corrections to gauge couplings from a field theory approach Original Research Article

Using an effective field theory approach, we address the effects on the gauge couplings of one and two additional compact dimensions in the presence of a constant background (gauge) field. Such background fields are a generic presence in models with extra dimensions and can be employed for gauge symmetry breaking mechanisms in the context of 4D N=1 supersymmetric models. The structure of the ultraviolet (UV) and infrared (IR) divergences that the gauge couplings develop in the presence of Wilson line vevʹs is investigated. One-loop radiative corrections to the gauge couplings due to overlapping effects of the compact dimensions and Wilson line vevʹs are computed for generic 4D N=1 models. Values of Wilson lines vevʹs corresponding to points (in the “moduli” space) of enhanced gauge symmetry cannot be smoothly reached perturbatively from those corresponding to the broken phase. The one-loop corrections are compared to their (heterotic) string counterpart in the “field theory” limit α′→0 to show remarkably similar results when no massless states are present in a Kaluza–Klein tower. An additional correction to the gauge coupling exists in the effective field theory approach when for specific Wilson lines vevʹs massless Kaluza–Klein states are present. This correction is not recoverable by the limit α′→0 of the (infrared regularised) string because the infrared regularisation limit and the limit α′→0 of the string result do not commute.