Neutrino Majorana Masses from String Theory Instanton Effects

TL;DR

The authors propose that right-handed neutrino Majorana masses can arise non-perturbatively from D-brane instantons in string compactifications where U(1)_{B-L} becomes massive via a Stückelberg mechanism. They derive precise zero-mode and intersection-number conditions that ensure gauge invariance and demonstrate this with an explicit toroidal intersecting-brane model, highlighting strong topological constraints (e.g., three generations) and the potential to lift unwanted zero modes via fluxes. They further discuss how similar instanton effects can generate the MSSM μ-term and other perturbatively forbidden couplings, and argue that this mechanism naturally implies R-parity in SUSY scenarios. Overall, the work shows how stringy instantons can furnish Majorana masses and shape realistic model-building in string theory.

Abstract

Finding a plausible origin for right-handed neutrino Majorana masses in semirealistic compactifications of string theory remains one of the most difficult problems in string phenomenology. We argue that right-handed neutrino Majorana masses are induced by non-perturbative instanton effects in certain classes of string compactifications in which the $U(1)_{B-L}$ gauge boson has a Stückelberg mass. The induced operators are of the form $e^{-U}ν_Rν_R$ where $U$ is a closed string modulus whose imaginary part transforms appropriately under $B-L$. This mass term may be quite large since this is not a gauge instanton and $Re U$ is not directly related to SM gauge couplings. Thus the size of the induced right-handed neutrino masses could be a few orders of magnitude below the string scale, as phenomenologically required. It is also argued that this origin for neutrino masses would predict the existence of R-parity in SUSY versions of the SM. Finally we comment on other phenomenological applications of similar instanton effects, like the generation of a $μ$-term, or of Yukawa couplings forbidden in perturbation theory.

Figures (4)

• Figure 1: Instanton induced right-handed neutrino Majorana mass term.
• Figure 2: World-sheet disk amplitude inducing a cubic coupling on the D2-brane instanton action. The cubic coupling involves the right-handed neutrinos lying at the intersection of the $c$ and $d^*$ D6-branes, and the two instanton fermion zero modes $\alpha$ and $\gamma$ from the D2-D6 intersections.
• Figure 3: The figure shows the D2-brane instanton (continuous line) and the $c^*$ and $d$ D6-branes at whose intersections lie the right-handed neutrinos. The instanton zero modes from the D2-D6 open strings are denoted by $\alpha$ and $\gamma$. The yellow areas describe (the projections of) the open string disk inducing a cubic coupling on the D2-brane instanton action.
• Figure 4: Disk amplitudes contributing cubic couplings between the D2-brane instanton fermion zero modes $\alpha^i$, $\gamma$, $\sigma$, and the spacetime Higgs fields $H$, $\overline H$. Upon integration over the fermion zero modes, the induced effective operator is a $\mu$-term.