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

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 K\"ahler 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.