Stringy Instantons and Yukawa Couplings in MSSM-like Orientifold Models

TL;DR

The paper tackles the problem that many MSSM-like Yukawa couplings vanish in D-brane realizations due to global $U(1)$ symmetries. It demonstrates how stringy $E2$-instantons can non-perturbatively generate these couplings, analyzing three four-stack quiver configurations and providing local realizations on a rigid $T^6/(\,\mathbb{Z}_2\times\mathbb{Z}_2')$ orientifold with torsion. It finds that Yukawa textures with realistic hierarchies can be achieved, particularly in the triangle quiver with a doubled Higgs sector, where instanton-induced $\mu$-terms can factorize and leave the MSSM Higgs light. The work highlights both the potential and limitations of these local models, noting the need for global embeddings and mechanisms for Majorana masses. Overall, it advances the understanding of non-perturbative Yukawa generation in MSSM-like string vacua and points to promising directions for fully realistic, globally consistent constructions.

Abstract

Type IIA orientifold constructions with intersecting D6-branes and their IIB duals in terms of magnetized D9/D7-branes constitute one of the most promising avenues for the construction of semirealistic MSSM-like compactifications. One generic problem with these constructions is, that there are many Yukawa couplings, which vanish due to additional U(1) symmetries in the theory. In this paper we consider a number of such settings and study, under what conditions stringy instanton effects can give rise to non-perturbative contributions to the Yukawa couplings, so that all perturbatively forbidden terms are induced. We find specific settings, in which indeed Yukawa couplings for all fermions are obtained. For some cases we provide specific local examples of rigid O(1) Instantons within the T^6/ Z2 x Z2' toroidal orientifold with torsion, giving rise to the required amplitudes. A potential problem in these settings is, that the same instantons, providing for Yukawa coupling contributions, may give rise to too large mu-terms for the Higgs multiplets. We show how this problem may be overcome in explicit models with a doubled Higgs system.

Figures (8)

• Figure 1: Instanton induced of the Yukawa coupling $l^I\, H_u \, N^J_R$ for the square quiver.
• Figure 2: Instanton induced Yukawa coupling $Q_L\, H_u \, u_R$ for the square quiver.
• Figure 3: Instanton induced Yukawa coupling $Q_L\, H_u \, u^I_R$ for the triangle quiver.
• Figure 4: Non perturbative generation of the $\mu$-term for the triangle quiver.
• Figure 5: Non-perturbative generation of $\mu$-term matrix $\mu^{IJ}$.