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

TL;DR

This work achieves a concrete, first-principles computation of D2-brane instanton effects in Type IIA orientifolds with intersecting D6-branes to generate non-perturbative superpotential couplings, notably Majorana masses for right-handed neutrinos. Using detailed CFT techniques, it shows that rigid, supersymmetric $E2$-instantons can absorb charged zero modes to produce terms of the form $W_{np}=\prod_i \Phi_i\, e^{-S_{E2}}$, while respecting global $U(1)$ charges via $Q_a(E2)$. In a local toroidal model on $T^6/({\mathbb Z}_2\times{\mathbb Z}_2')$ with discrete torsion, the authors construct a toy SU(5)-like GUT setup in which 8 invariant, rigid instantons contribute to Majorana masses for right-handed neutrinos in the $10^{11}$ GeV range, enabling a see-saw mechanism when Dirac masses are perturbatively realized. The results demonstrate the viability of stringy non-perturbative physics to generate phenomenologically relevant mass scales and outline the significant challenges in achieving globally consistent vacua that realize these effects in full realism.

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 mu-terms. These results can readily be extended to higher-dimensional operators. In concrete realizations of such non-perturbative 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/(Z_2 x 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 non-perturbative couplings give rise to the see-saw mechanism.

Figures (4)

• Figure 1: Example of family structure yielding diagonal and off-diagonal fermion bilinears.
• Figure 2: $T^6/\mathbb{Z}_2\times \mathbb{Z}_2'$ with $\beta^1=\beta^2= \beta^3=0$.
• Figure 3: Intersection pattern in first torus.
• Figure 4: Intersection pattern in second and third torus.