  It was found that deformation of S^7 gives rise to renormalization group(RG)
flow from N=8, SO(8)-invariant UV fixed point to N=1, G_2-invariant IR fixed
point in four-dimensional gauged N=8 supergravity. Also BPS supersymmetric
domain wall configuration interpolated between these two critical points. In
this paper, we use the G_2-invariant RG flow equations for both scalar fields
and domain-wall amplitude and apply them to the nonlinear metric ansatz
developed by de Wit, Nicolai and Warner some time ago. We carry out the
M-theory lift of the G_2-invariant RG flow through a combinatoric use of the
four-dimensional RG flow equations and eleven-dimensional Einstein-Maxwell
equations. The nontrivial r(that is the coordinate transverse to the domain
wall)-dependence of vacuum expectation values becomes consistent with not only
at the critical points but also along the supersymmetric RG flow connecting two
critical points. By applying an ansatz for an eleven-dimensional three-form
gauge field with varying scalars, we discover an exact solution to the
eleven-dimensional Einstein-Maxwell equations corresponding to the M-theory
lift of the G_2-invariant RG flow.
