On Gauge couplings, "Large" extra-dimensions and the limit alpha'->0 of the String

Using an effective field theory (EFT) approach for a generic model with two additional dimensions compactified on a two-torus, we compute the total one-loop radiative corrections to the gauge couplings due to associated Kaluza-Klein massive and massless states. A consistent treatment of both infrared (IR) and ultraviolet (UV) divergences shows a connection via infrared regulator effects between the massless and massive sectors of a compactified theory. A new correction to the gauge couplings is found such that their UV behaviour is sensitive to IR regulator dependent effects in the sector of (infinitely many) massive modes. This correction is a one-loop UV-IR mixing effect due to infinitely many Kaluza-Klein modes and exists for two compact dimensions. The link with string theory is addressed to show that this correction, logarithmic in the UV scale, cannot be recovered from known (infrared regularised) string calculations in the field theory ``limit'' alpha'->0. We explain the origin of this discrepancy and address some of its implications.