Kinetic mixing of U(1)s for local string models

TL;DR

This work demonstrates that kinetic mixing between massless U(1) gauge factors can arise in local string models with D3-branes at toroidal orbifold singularities, driven by winding modes in the ${\cal N}=2$ sector. Using a background-field method, the authors connect the 1-loop annulus amplitudes to the mixing parameter $\chi$, showing that $\chi$ depends on the complex structure modulus and the geometry of brane separations, but is independent of Kähler moduli due to holomorphy. They provide explicit analyses for ${\mathbb{T}}^6/\mathbb{Z}_4$ and ${\mathbb{T}}^6/\mathbb{Z}_6'$ and find that kinetic mixing is possible when U(1)’s live on at least two singularities with nonuniform separations, while it is suppressed or absent in equidistant configurations such as ${\mathbb{Z}}_6$ and ${\Delta}_{27}$. The paper also discusses the relation to gauge-threshold corrections and outlines general criteria for kinetic mixing across a broader class of orbifolds, with implications for hidden-sector phenomenology and hypercharge embedding.

Abstract

We study kinetic mixing between massless U(1)s in toroidal orbifolds with D3-branes at orbifold singularities. We focus in particular on C^3/Z_4 singularities but also study C^3/Z_6 and C^3/Z'_6 singularities. We find kinetic mixing can be present and describe the conditions for it to occur. Kinetic mixing comes from winding modes in the N=2 sector of the orbifold. If kinetic mixing is present its size depends only on the complex structure modulus of the torus and is independent of the Kähler moduli. We also study gauge threshold corrections for local Z_M x Z_N orbifold models finding that, consistent with previous studies, gauge couplings run from the bulk winding scale rather than the string scale.