Quantum Horizons of the Standard Model Landscape
Nima Arkani-Hamed, Sergei Dubovsky, Alberto Nicolis, Giovanni Villadoro
TL;DR
We show that SM+GR has a landscape of lower-dimensional vacua beyond the unique 4D vacuum, realized via circle compactification with Casimir-induced modulus stabilization. In the Majorana neutrino case, there exists a near-continuous set of AdS$_3\times S_1$ vacua with circumference $~$20$\,\mu\mathrm{m}$ and AdS$_3$ length $4\times 10^{25}$\,m, and AdS/CFT implies a $CFT_2$ with central charge $c \sim 10^{90}$ whose physics matches the 4D vacuum for energies between $E \in [10^{-1}\ \mathrm{eV}, 10^{48}\ \mathrm{GeV}]$. The AdS vacua can be realized as near-horizon regions of quantum extremal black objects in higher dimensions, made possible by Casimir-violation of the null-energy condition; these include near-critical black strings and near-critical black holes, with extremal 3D horizons that are (meta)stable and have an entropy independent of $\hbar$ and $G_N$, enabling potential microscopic counting as $G_N\to 0$. The work suggests the broader AdS landscape can be embedded in string theory as near-horizon geometries of extremal black branes, linking modulus stabilization, holography, and horizon physics in the Standard Model context.
Abstract
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 AdS3xS1 vacua, with circumference ~20 microns and AdS3 length 4x10^25 m. By AdS/CFT, there is a CFT2 of central charge c~10^90 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 10^48 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 hbar 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.