U(1) mixing and D-brane linear equivalence

Linear equivalence is a criterion that compares submanifolds in the same homology class. We show that, in the context of type II compactifications with D-branes, this concept translates to the kinetic mixing between U(1) gauge symmetries arising in the open and closed string sectors. We argue that in generic D-brane models such mixing is experimentally detectable through the existence of milli-charged particles. We compute these gauge kinetic functions by classifying the 4d monopoles of a compactification and analyzing the Witten effect on them, finding agreement with previous results and extending them to more general setups. In particular, we compute the gauge kinetic functions mixing bulk and magnetized D-brane U(1)'s and derive a generalization of linear equivalence for these objects. Finally, we apply our findings to F-theory SU(5) models with hypercharge flux breaking.