Computation of D-brane instanton induced superpotential couplings: Majorana masses from string theory

Abstract

We perform a detailed conformal field theory analysis of $D2$-brane instanton effects in four-dimensional type IIA string vacua with intersecting $D6$-branes. In particular, we explicitly compute instanton induced fermion two-point couplings which play the role of perturbatively forbidden Majorana mass terms for right-handed neutrinos or MSSM $\ensuremath{\mu}$ terms. These results can readily be extended to higher-dimensional operators. In concrete realizations of such nonperturbative effects, the Euclidean $D2$-brane has to wrap a rigid, supersymmetric cycle with strong constraints on the zero-mode structure. Their implications for type IIA compactifications on the ${T}^{6}/({\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2})$ orientifold with discrete torsion are analyzed. We also construct a local supersymmetric GUT-like model allowing for a class of Euclidean $D2$-branes whose fermionic zero modes meet all the constraints for generating Majorana masses in the phenomenologically allowed regime. Together with perturbatively realized Dirac masses, these nonperturbative couplings give rise to the seesaw mechanism.