Bulk Gauge Fields and Holographic RG from Exact RG
arXiv:2201.06240 · doi:10.1007/JHEP02(2023)174
Abstract
Recently, a method was described for deriving Holographic RG equation in space starting from an Exact RG equation of a -dimensional boundary CFT (Sathiapalan, Sonoda, 2017). The evolution operator corresponding to the Exact RG equation was rewritten as a functional integral of a dimensional field theory in space. This method has since been applied to elementary scalars and composite scalars in the 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 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.
arXiv commentv3: added important references, and made precise a few vague statements regarding standard and alternate quantisations
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