Spacetime Instanton Corrections in 4D String Vacua - The Seesaw Mechanism for D-Brane Models

TL;DR

The paper develops a systematic framework for spacetime instanton corrections in 4D string vacua, focusing on E2-instantons in Type IIA intersecting D-brane models. It shows how gauge invariance and fermionic zero-mode counting constrain non-perturbative superpotential terms and explains the computation via disc amplitudes for boundary-changing operators multiplied by a one-loop determinant, yielding couplings of the form $W \simeq \prod_i \Phi_i\, e^{-S_{\mathrm{E2}}}$. The authors demonstrate that these instantons can generate Majorana masses for right-handed neutrinos and other perturbatively forbidden terms, enabling a seesaw mechanism, while also discussing potential vacuum destabilisation and higher-derivative corrections. They extend the analysis to Type IIB and heterotic duals and discuss phenomenological implications for MSSM-like models, including neutrino masses, the $\mu$-term, and proton-decay operators, highlighting the role of cycle volumes and instanton actions in setting scales. The work provides a concrete bridge between non-perturbative string effects and low-energy phenomenology, with implications for moduli stabilization and the broader string landscape.

Abstract

We systematically investigate instanton corrections from wrapped Euclidean D-branes to the matter field superpotential of various classes of N=1 supersymmetric D-brane models in four dimensions. Both gauge invariance and the counting of fermionic zero modes provide strong constraints on the allowed non-perturbative superpotential couplings. We outline how the complete instanton computation boils down to the computation of open string disc diagrams for boundary changing operators multiplied by a one-loop vacuum diagram. For concreteness we focus on E2-instanton effects in Type IIA vacua with intersecting D6-branes, however the same structure emerges for Type IIB and heterotic vacua. The instantons wrapping rigid cycles can potentially destabilise the vacuum or generate perturbatively absent matter couplings such as proton decay operators, mu-parameter or right-handed neutrino Majorana mass terms. The latter allow the realization of the seesaw mechanism for MSSM-like intersecting D-brane models.

Figures (7)

• Figure 1: Standard disc tadpole
• Figure 2: Leading and subleading disc diagrams for $\phi_{ab}\phi_{cd}$ coupling. Only the leading order two-disc amplitude contributes to the superpotiential.
• Figure 3: Coupling $\phi_{ab}$ absorbing four fermionic zero modes
• Figure 4: Coupling $\phi_{a,x_1}\phi_{x_1, x_2}\ldots \phi_{x_n,b}$ and disc tadpole with D6-brane moduli insertions
• Figure 5: Series of 1-loop contributions for the example of only two D6-branes