Instanton Induced Neutrino Majorana Masses in CFT Orientifolds with MSSM-like spectra

Recently it has been shown that string instanton effects may give rise to neutrino Majorana masses in certain classes of semi-realistic string compactifications. In this paper we make a systematic search for supersymmetric MSSM-like Type II Gepner orientifold constructions admitting boundary states associated with instantons giving rise to neutrino Majorana masses and other L- and/or B-violating operators. We analyze the zero mode structure of D-brane instantons on general type II orientifold compactifications, and show that only instantons with O(1) symmetry can have just the two zero modes required to contribute to the 4d superpotential. We however discuss how the addition of fluxes and/or possible non-perturbative extensions of the orientifold compactifications would allow also instantons with $Sp(2)$ and U(1) symmetries to generate such superpotentials. In the context of Gepner orientifolds with MSSM-like spectra, we find no models with O(1) instantons with just the required zero modes to generate a neutrino mass superpotential. On the other hand we find a number of models in one particular orientifold of the Gepner model $(2,4,22,22)$ with $Sp(2)$ instantons with a few extra uncharged non-chiral zero modes which could be easily lifted by the mentioned effects. A few more orientifold examples are also found under less stringent constraints on the zero modes. This class of $Sp(2)$ instantons have the interesting property that R-parity conservation is automatic and the flavour structure of the neutrino Majorana mass matrices has a simple factorized form.