Regularisation Techniques for the Radiative Corrections of Wilson lines and Kaluza-Klein states

TL;DR

This paper analyzes one-loop gauge coupling corrections in orbifold compactifications with Wilson lines using three regularisation schemes, providing a general framework applicable to various models and discussing implications for string theory and unification.

Contribution

It presents a comprehensive calculation of one-loop corrections in orbifold models with Wilson lines across multiple regularisation schemes, enhancing the understanding of gauge coupling renormalization.

Findings

Results are consistent across DR, ZR, and PT schemes.

Corrections can be applied broadly to orbifold compactifications.

Implications for gauge coupling unification are discussed.

Abstract

Within an effective field theory framework we compute the most general structure of the one-loop corrections to the 4D gauge couplings in one- and two-dimensional orbifold compactifications with non-vanishing constant gauge background (Wilson lines). Although such models are non-renormalisable, we keep the analysis general by considering the one-loop corrections in three regularisation schemes: dimensional regularisation (DR), Zeta-function regularisation (ZR) and proper-time cut-off regularisation (PT). The relations among the results obtained in these schemes are carefully addressed. With minimal re-definitions of the parameters involved, the results obtained for the radiative corrections can be applied to most orbifold compactifications with one or two compact dimensions. The link with string theory is discussed. We mention a possible implication for the gauge couplings unification in such models.