Bino-wino coannihilation as a prediction in the $E_7$ unification of
  families
  We study the phenomenological consequences of the supersymmetric (SUSY)
$E_7/SU(5)\times U(1)^3$ non-linear sigma model coupled to supergravity, where
the three generations of quark and lepton chiral multiplets appear as (pseudo)
Nambu Goldstone (NG) multiplets, that is, the origin of the three families is
explained. To break SUSY, we introduce a SUSY breaking field charged under some
symmetry avoiding the Polonyi problem. The gaugino mass spectrum is almost
uniquely determined when one requires the electroweak vacuum to be
(meta)stable: it would be a miracle that the mass difference between the bino
and wino turns out to be within $O(1)\%$ at the low energy. Thus, a bino-wino
coannihilation is naturally predicted, which can explain the correct relic
abundance of dark matter. Moreover, we find that the bottom-tau Yukawa
couplings and the gauge couplings are unified up to $O(1)\%$ in most of the
viable region. This scenario can be fully tested at the LHC and future collider
experiments since the gauginos and some of the pseudo-NG bosons are light. An
axion-like multiplet, which can be identified with the QCD axion, is also
predicted.
