Bulk Gauge Fields and Holographic RG from Exact RG

TL;DR

This paper extends a method for deriving holographic RG equations from exact RG equations to include bulk gauge fields and gravity, providing a new perspective on the AdS/CFT correspondence without relying on the conjecture.

Contribution

It applies the exact RG approach to conserved currents and energy-momentum tensors, deriving bulk gauge and gravitational actions at the free level.

Findings

Derived Maxwell and Einstein actions from boundary CFT operators.

Extended the exact RG framework to include gauge fields and gravity.

Provided a non-conjectural derivation of bulk dynamics from boundary data.

Abstract

Recently, a method was described for deriving Holographic RG equation in $AdS_{D+1}$ space starting from an Exact RG equation of a $D$-dimensional boundary CFT (Sathiapalan, Sonoda, 2017). The evolution operator corresponding to the Exact RG equation was rewritten as a functional integral of a $D+1$ dimensional field theory in $AdS_{D+1}$ space. This method has since been applied to elementary scalars and composite scalars in the $O(N)$ model (Sathiapalan, 2020). In this paper, we apply this technique to the conserved vector current and the energy momentum tensor of a boundary CFT, the $O(N)$ model at a fixed point. These composite spin one and spin two operators are represented by auxiliary fields and extend into the bulk as gauge fields and metric perturbations. We obtain, at the free level, the (gauge fixed) Maxwell and Einstein actions. While the steps involved are motivated by the AdS/CFT correspondence, none of the steps logically require the AdS/CFT conjecture for their justification.