  We describe a one-parameter family of new holographic RG flows that start
from $AdS_4 \times S^7$ and go to $\widehat{AdS_5} \times {\cal B}_6$, where
${\cal B}_6$ is conformal to a K\"ahler manifold and $\widehat{AdS_5}$ is
Poincar\'e $AdS_5$ with one spatial direction compactified and fibered over
${\cal B}_6$. The new solutions "flow up dimensions," going from the
$(2+1)$-dimensional conformal field theory on M2 branes in the UV to a
$(3+1)$-dimensional field theory on intersecting M5 branes in the infra-red.
The M2 branes completely polarize into M5 branes along the flow and the
Poincar\'e sections of the $\widehat{AdS_5}$ are the $(3+1)$-dimensional common
intersection of the M5 branes. The emergence of the extra dimension in the
infra-red suggests a new strongly-coupled phase of the M2 brane and ABJM
theories in which charged solitons are becoming massless. The flow solution is
first analyzed by finding a four-dimensional $N \! = \! 2$ supersymmetric flow
in $N \! = \! 8$ gauged supergravity. This is then generalized to a one
parameter family of non-supersymmetric flows. The infra-red limit of the
solutions appears to be quite singular in four dimensions but the uplift to
eleven-dimensional supergravity is remarkable and regular (up to orbifolding).
Our construction is a non-trivial application of the recently derived uplift
formulae for fluxes, going well beyond the earlier constructions of stationary
points solutions. The eleven-dimensional supersymmetry is also analyzed and
shows how, for the supersymmetric flow, the M2-brane supersymmetry in the UV is
polarized entirely into M5-brane supersymmetry in the infra-red.
