Realistic Yukawa Couplings through Instantons in Intersecting Brane Worlds

TL;DR

This paper demonstrates how E2-instantons in intersecting D6-brane models can generate realistic Yukawa couplings, overcoming the rank one problem and potentially explaining observed hierarchies.

Contribution

It provides a detailed instanton calculus framework for D-brane models, showing how instantons can produce realistic Yukawa textures and resolve the rank one issue.

Findings

E2-instantons generate non-zero Yukawa couplings for previously massless states.

The approach offers a geometric explanation for Yukawa hierarchy.

The paper supplies the necessary instanton calculus tools for these models.

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.