Sterile neutrinos, black hole vacuum and holographic principle

We construct an effective field theory (EFT) model that describes matter field interactions with Schwarzschild mini-black-holes (SBH’s), treated as a scalar field, $$B_0(x)$$ B 0 ( x ) . Fermion interactions with SBH’s require a complex spurion field, $$\theta _{ij}$$ θ ij , which we interpret as the EFT description of “holographic information,” which is correlated with the SBH as a composite system. We consider Hawking’s virtual black hole vacuum (VBH) as a Higgs phase, $$\langle B_0 \rangle =V$$ ⟨ B 0 ⟩ = V . Integrating sterile neutrino loops, the information field $$\theta _{ij}$$ θ ij is promoted to a dynamical field, necessarily developing a tachyonic instability and acquiring a VEV of order the Planck scale. For N sterile neutrinos this breaks the vacuum to $$SU(N)\times U(1)/SO(N)$$ S U ( N ) × U ( 1 ) / S O ( N ) with N degenerate Majorana masses, and $$\frac{1}{2}N(N+1)$$ 1 2 N ( N + 1 ) Nambu-Goldstone neutrino-Majorons. The model suggests many scalars fields, corresponding to all fermion bilinears, may exist bound nonperturbatively by gravity.