U(1) mixing and D-brane linear equivalence
Fernando Marchesano, Diego Regalado, Gianluca Zoccarato
TL;DR
This work establishes a direct link between D-brane linear equivalence and kinetic mixing between open-string U(1) gauge factors and bulk RR U(1)s in type II compactifications. By analyzing 4d monopoles and employing the Witten effect, the authors derive holomorphic gauge-kinetic functions that encode open–closed mixing through simple chain- and relative-homology data, applicable to both IIA D6-branes and IIB magnetized D7-branes, and extended to F-theory hypercharge flux. A unified description via generalized geometry and relative cohomology is developed, enabling a robust calculation of open–closed mixing and the identification of a generalized notion of linear equivalence, with explicit formulas for the mixing in various setups, including hypercharge in F-theory GUTs. The results imply possible milli-charged signatures and potential refinements to gauge coupling unification, highlighting testable consequences and providing a framework for model-independent predictions in string phenomenology.
Abstract
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.