Emergent dual holographic description for interacting Dirac fermions in the large N limit

Abstract

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.