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 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.