  We propose a method to give a $d+1$ geometry from a $d$ dimensional quantum
field theory in the large N expansion. We first construct a $d+1$ dimensional
field from the $d$ dimensional one using the gradient flow equation, whose flow
time $t$ represents the energy scale of the system such that $t\rightarrow 0$
corresponds to the ultra-violet (UV) while $t\rightarrow\infty$ to the
infra-red (IR). We define the induced metric using $d+1$ dimensional field
operators. We show that the metric defined in this way becomes classical in the
large N limit: quantum fluctuations of the metric are suppressed as 1/N due to
the large $N$ factorization property. As a concrete example, we apply our
method to the O(N) non-linear $\sigma$ model in two dimensions. We calculate
the three dimensional induced metric, which describes an AdS space in the
massless limit. We finally discuss several open issues for future
investigations.
