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.
Highlights
Scenarios that are the most generic in the plethora of semi-realistic string vacua, and to compute the most robust testable quantities associated to them
In our analysis of type IIA compactifications we have found that the kinetic mixing between open and closed string U(1)’s can be computed by means of a simple chain formula, whose physical meaning can be understood as the Witten effect applied to D-brane U(1) monopoles
Our generalization including the kinetic mixing fY t provides an even more flexible scheme to fix such discrepancy. Motivated by their implications for the existence of milli-charged particles, in this paper we have analyzed the kinetic mixing between closed string U(1)’s and those associated with D-branes in Type II orientifolds
Summary
The variation comes from assuming the presence of a further U(1) gauge symmetry that does not arise from the D-brane degrees of freedom, but rather from the Kaluza-Klein reduction of the Ramond-Ramond closed string sector of the theory Such bulk U(1)’s, dubbed RR photons in [23], exist for generic choices of the compactification manifold M6 and are natural sources of hidden U(1) gauge symmetries, because the only particles charged under them are extremely heavy: namely D-branes wrapped on internal cycles and point-like in 4d. Because these are equivalent to bound states of D-branes of different dimension, the concept of linear equivalence is more complicated and we need to use the machinery of generalized geometry to properly formulate the kinetic mixing. We discuss the relation between open-closed kinetic mixing and linear equivalence of cycles (see appendix A)
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