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 quantumstabilized 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 GN , so a microscopic counting of the entropy may be possible in the GN → 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.