Bulk and brane radiative effects in gauge theories on orbifolds
G. v. Gersdorff, N. Irges, M. Quiros
TL;DR
This work analyzes one-loop bulk and brane radiative corrections in a 5D gauge theory on ${ m M}_4 imes S^1/{ m Z}_2$ with gauge group ${ m G}$ broken to ${ m H}$ by the orbifold. It demonstrates that no quadratic divergences arise for either bulk or brane mass terms, with bulk Higgs masses finite and able to trigger Hosotani-induced breaking of ${ m H}$ depending on fermion content, while brane Higgs masses vanish at one loop. The study also clarifies that gauge-field KK masses renormalize only logarithmically at one loop, whereas brane-localized effects may induce finite wave-function renormalization and two-loop Higgs corrections, pointing to a consistent higher-dimensional solution to the hierarchy problem at this order. The Hosotani mechanism emerges as a central tool for spontaneous gauge symmetry breaking in this setting, with the potential to reduce rank and generate rich phenomenology on the branes, contingent on the detailed fermion representations and flavor content. Overall, the results support a scenario where the UV sensitivity is controlled by the compactification scale $1/R$, though radius stabilization and genuine two-loop effects remain important avenues for future work.
Abstract
We have computed one-loop bulk and brane mass renormalization effects in a five-dimensional gauge theory compactified on the M_4 \times S^1/Z_2 orbifold, where an arbitrary gauge group G is broken by the orbifold action to its subgroup H. The space-time components of the gauge boson zero modes along the H generators span the gauge theory on the orbifold fixed point branes while the zero modes of the higher-dimensional components of the gauge bosons along the G/H generators play the role of Higgs fields with respect to the gauge group H. No quadratic divergences in the mass renormalization of the gauge and Higgs fields are found either in the bulk or on the branes. All brane effects for the Higgs field masses vanish (only wave function renormalization effects survive) while bulk effects are finite and can trigger, depending on the fermionic content of the theory, spontaneous Hosotani breaking of the brane gauge group H. For the gauge fields we do find logarithmic divergences corresponding to mass renormalization of their heavy Kaluza-Klein modes. Two-loop brane effects for Higgs field masses are expected from wave function renormalization brane effects inserted into finite bulk mass corrections.