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Fuzzy dark matter and neutron Majorana mass from gravitational instantons

We explore the possibility that a super-light candidate for fuzzy (or wave) Dark Matter (fDM) may be a new composite boson state of fermions, rather than an axion-like Bose-Einstein condensate. We start from string-inspired massless Majorana fermions χ thought as super-modulini fields from string compactifications. We show that massless (or nearly massless) fermions can form a Bose-Einstein condensate and they can acquire a tiny mass term from quantum-gravitational non-perturbative effects such as gravitational instantons. For having a successful candidate for fDM, the so generated Majorana mass is , or so; otherwise decoherence would suppress quantum-mechanical effects in the macroscopic limit. Gravity is democratically coupled with every standard model particles; any neutral fermions acquire a Majorana mass equal to . While for neutrinos, such a mass would be completely out of any testability, a neutron Majorana mass can also be envisaged. A gravitational Majorana mass for the neutron generates baryon violating neutron-antineutron oscillations. Contrary to other competitive models, here the transition is generated without adding any new particles or interactions to the standard model: it is a genuine quantum gravity effect. Current limits on imply a Majorana mass bound and, therefore, the very same limit on the Gravi-fuzzy DM (GfDM) candidate. The next generation of experiments searching for can probe up to the , potentially excluding Gravi-fuzzy DM up to it.