Realistic Yukawa Couplings through Instantons in Intersecting Brane Worlds
Steven A. Abel, Mark D. Goodsell
TL;DR
Realistic Yukawa couplings in intersecting D-brane models can be achieved by one-loop E2-instanton corrections to Yukawa couplings, which lift the rank-one problem. The authors develop the instanton calculus on toroidal orientifolds, showing that the nonperturbative Yukawa piece $Y^{np}_{ab}$ has rank 3 and is exponentially suppressed by $e^{-S^0_{E2}}$ relative to perturbative terms, yielding a hierarchical texture: $Y_{ab} = Y^0_{ab} + Y^{np}_{ab}$. The calculation hinges on the interplay of holomorphic Pfaffian/determinant factors, worldsheet instantons, and constraints on zero modes; it also discusses potential links to Majorana neutrino masses and the μ-term. The results provide a concrete, geometry-driven mechanism for Yukawa hierarchies and a computable framework for extracting Yukawa textures from the compactification data.
Abstract
The Yukawa couplings of the simpler models of D-branes on toroidal orientifolds suffer from the so-called ``rank one'' problem -- there is only a single non-zero mass and no mixing. We consider the one-loop contribution of E2-instantons to Yukawa couplings on intersecting D6-branes, and show that they can solve the rank one problem. In addition they have the potential to provide a geometric explanation for the hierarchies observed in the Yukawa coupling. In order to do this we provide the necessary quantities for instanton calculus in this class of background.