Sterile neutrinos, black hole vacuum and holographic principle

Abstract

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). Fermion interactions with SBH’s require a 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 Hawking’s virtual black hole vacuum (VBH) as a Higgs phase, langle B_0 rangle =V. Integrating sterile neutrino loops, the information 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 frac{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.