Quantum horizons of the standard model landscape

The long-distance effective field theory of our Universe—the Standard Model coupled to gravity—has a unique 4D vacuum, but we show that it also has a landscape of lower-dimensional vacua, with the potential for moduli arising from vacuum and Casimir energies. For minimal Majorana neutrino masses, we find a near-continuous infinity of AdS₃ × S₁ vacua, with circumference ∼ 20 microns and AdS₃ length 4 × 10²⁵ m. By AdS/CFT, there is a CFT₂ of central charge c ∼ 10⁹⁰ which contains the Standard Model (and beyond) coupled to quantum gravity in this vacuum. Physics in these vacua is the same as in ours for energies between 10⁻¹ eV and 10⁴⁸ GeV, so this CFT₂ also describes all the physics of our vacuum in this energy range. We show that it is possible to realize quantum-stabilized AdS vacua as near-horizon regions of new kinds of quantum extremal black objects in the higher-dimensional space—near critical black strings in 4D, near-critical black holes in 3D. The violation of the null-energy condition by the Casimir energy is crucial for these horizons to exist, as has already been realized for analogous non-extremal 3D black holes by Emparan, Fabbri and Kaloper. The new extremal 3D black holes are particularly interesting—they are (meta)stable with an entropy independent of ℏ and G_N, so a microscopic counting of the entropy may be possible in the G_N → 0 limit. Our results suggest that it should be possible to realize the larger landscape of AdS vacua in string theory as near-horizon geometries of new extremal black brane solutions.