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 (SBHs), treated as a scalar field, $B_0(x)$. Fermion interactions with SBHs require a random complex spurion field, $theta_{ij}$, which we interpret as the EFT description of holographic information, which is correlated with the SBH as a composite system. We consider Hawkings virtual black hole vacuum (VBH) as a Higgs phase, $langle B_0 rangle =V$. Integrating sterile neutrino loops, the field $theta_{ij}$ 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 $SU(N)times U(1)/SO(N)$ with $N$ degenerate Majorana masses, and $(1/2)N(N+1)$ Nambu-Goldstone neutrino-Majorons. The model suggests many scalars fields, corresponding to all fermion bilinears, may exist bound nonperturbatively by gravity.