Wilson lines corrections to gauge couplings from a field theory approach

TL;DR

This paper investigates how Wilson line backgrounds in extra dimensions affect gauge couplings using an effective field theory approach, revealing divergences, corrections, and their relation to string theory results.

Contribution

It provides a detailed field theory calculation of one-loop gauge coupling corrections due to Wilson lines and extra dimensions, comparing with string theory predictions.

Findings

Wilson lines induce specific UV and IR divergences in gauge couplings.

One-loop corrections match string theory results in certain limits.

Massless Kaluza-Klein states cause additional gauge coupling corrections.

Abstract

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 vev's is investigated. One-loop radiative corrections to the gauge couplings due to overlapping effects of the compact dimensions and Wilson line vev's are computed for generic 4D N=1 models. Values of Wilson lines vev's corresponding to points (in the ``moduli'' space) of enhanced gauge symmetry cannot be smoothly reached {\it perturbatively} from those corresponding to the broken phase. The one-loop corrections are compared to their (heterotic) string counterpart in the ``field theory'' limit alpha'->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 vev's massless Kaluza-Klein states are present. This correction is not recoverable by the limit alpha'->0 of the (infrared regularised) string because the infrared regularisation limit and the limit alpha'->0 of the string result do not commute.