Holographic dual of free field theory

TL;DR

The paper derives a holographic dual for free field theories in arbitrary dimensions by reinterpreting the exact renormalization group as dynamics on AdS_{D+1} and formulating a higher-spin gravity description with hs(D-1,2) gauge symmetry. It introduces bilocal sources and a cutoff kernel, recasts the RG flow as a flat higher-spin connection with a covariantly constant bilocal field, and shows that the on-shell bulk holonomy reproduces all boundary correlation functions. Although the bulk theory is not the standard higher-spin action, the framework provides a concrete mechanism to compute correlators via bulk propagators and holonomies, bridging RG flow and holography. The work also outlines limitations and future directions, including covariant refinements and extensions to interacting O(N) models, with potential impact on understanding locality in AdS/CFT.

Abstract

We derive a holographic dual description of free quantum field theory in arbitrary dimensions, by reinterpreting the exact renormalization group, to obtain a higher spin gravity theory of the general type which had been proposed and studied as a dual theory. We show that the dual theory reproduces all correlation functions.

Figures (1)

• Figure 1: A graphic representation of the calculation of a four point correlator. The dashed line is the holonomy contour. $a$ and $b$ are two points on the boundary; one of which is taken to infinity. The (brown) lines represent boundary-to-bulk and bulk-to-bulk propagators.