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 nonperturbative 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.

• Received 10 March 2020
• Revised 8 September 2020
• Accepted 27 September 2020

DOI:https://doi.org/10.1103/PhysRevD.102.086014