Compact objects in and beyond the Standard Model from non-perturbative vacuum scalarization

We consider a theory in which a real scalar field is Yukawa-coupled to a fermion and has a potential with two non-degenerate vacua. If the coupling is sufficiently strong, a collection of N fermions deforms the true vacuum state, creating energetically-favored false-vacuum pockets in which fermions are trapped. We embed this model within General Relativity and prove that it admits self-gravitating compact objects where the scalar field acquires a non-trivial profile due to non-perturbative effects. We discuss some applications of this general mechanism: i) neutron soliton stars in low-energy effective QCD, which naturally happen to have masses around 2 solar masses and radii around 10 km even without neutron interactions; ii) Higgs false-vacuum pockets in and beyond the Standard Model; iii) dark soliton stars in models with a dark sector. In the latter two examples, we find compelling solutions naturally describing centimeter-size compact objects with masses around 10^-6 solar masses, intriguingly in a range compatible with the OGLE+HSC microlensing anomaly. Besides these interesting examples, the mechanism of non-perturbative vacuum scalarization may play a role in various contexts in and beyond the Standard Model, providing a support mechanism for new compact objects that can form in the early universe, can collapse into primordial black holes through accretion past their maximum mass, and serve as dark matter candidates.