Phenomenology of 1032 dark sectors

We postulate an exact permutation symmetry acting on 1032 standard model copies as the largest possible symmetry extension of the standard model. This setup automatically lowers the fundamental gravity cutoff down to TeV, and thus, accounts for the quantum stability of the weak scale. We study the phenomenology of this framework and show that below TeV energies the copies are well hidden, obeying all the existing observational bounds. Nevertheless, we identify a potential low energy window into the hidden world, the oscillation of the neutron into its dark copies. At the same time, proton decay can be suppressed by gauging the diagonal baryon number of the different copies. This framework offers an alternative approach to several particle physics questions. For example, we suggest a novel mechanism for generating naturally small neutrino masses that are suppressed by the number of neutrino species. The mirror copies of the standard model naturally house dark matter candidates. The general experimentally observable prediction of this scenario is an emergence of strong gravitational effects at the LHC. The low energy permutation symmetry powerfully constrains the form of this new gravitational physics and allows to make observational predictions, such as, production of micro black holes with very peculiar properties.