  We derive an effective dual holographic Einstein-Maxwell theory, applying
renormalization group transformations to interacting Dirac fermions in a
recursive way. In particular, we show how both background metric tensor and
U(1) gauge fields become dynamical to describe the renormalization group flows
of coupling functions and order parameter fields of the corresponding quantum
field theory through natural emergence of an extra-dimensional space,
respectively. Finally, we propose a prescription on how to calculate
correlation functions in a non-perturbative way, where quantum fluctuations of
both metric and gauge fields are frozen to cause a classical field theory of
the Einstein-Maxwell type in the large $N$ limit. Here, $N$ is the flavor
degeneracy of Dirac fermions. This prescription turns out to coincide with that
of the holographic duality conjecture.
