Emergent dual holographic description as a nonperturbative generalization of the Wilsonian renormalization group

Abstract

In holographic duality, dynamics along the emergent extra-dimensional space describes a renormalization group (RG) flow of the corresponding quantum field theory (QFT). Following this idea, we develop an emergent holographic description of a QFT, where not only the information of the RG flow is introduced into an IR holographic dual effective field theory (HDEFT), but also the UV information of the QFT is encoded in the HDEFT through the IR boundary condition. In particular, we argue that this dual holographic construction is self-consistent within the assumption of bulk locality, showing the following two aspects: The solution of the Hamilton-Jacobi equation is given by the IR boundary effective action, and the Ward identity involving the QFT energy-momentum tensor current is satisfied naturally. We discuss the role of the RG $\beta$-function in the bulk effective dynamics of the metric tensor near a conformally invariant fixed point. We claim that this emergent dual gravity theory generalizes the perturbative Wilsonian RG framework into a non-perturbative way.