Bulk modified gravity from a thermal CFT by the conformal flow

TL;DR

This paper constructs a bulk spacetime from a thermal boundary CFT using a conformal flow, revealing a modified gravity description near the boundary and a conformally related extremal black brane in the deep bulk.

Contribution

It introduces a method to derive bulk geometries from thermal CFTs and suggests the bulk gravity is a modified theory like $f(R)$ gravity, extending the usual Einstein gravity framework.

Findings

Bulk spacetime constructed via conformal flow from boundary CFT.

Near boundary, the spacetime is asymptotically AdS with scalar perturbations.

Deep in the bulk, spacetime resembles the near horizon of an extremal black brane.

Abstract

We construct a bulk spacetime from a boundary CFT, $O(N)$ free scalar model, at finite temperature using a smearing technique, called a conformal flow. The bulk metric is constructed as an information metric associated with the boundary thermal state. Near the boundary (UV region), an asymptotically AdS spacetime is obtained with a leading order perturbation of scalar mode. Based on the falloff behavior of the perturbations and the $O(N)$ symmetry in the CFT, we argue that the corresponding bulk theory is a modified gravity with scalar mode such as $f(R)$ gravity rather than Einstein's general relativity coupled minimally to matter fields. Moving to Einstein frame, we show that the metric is asymptotically the same as the AdS black brane solution. On the other hand, deep in the bulk (IR region), the spacetime turns out to be conformally equivalent to the near horizon limit of AdS extremal black brane, though it is no longer a solution of $f(R)$ gravity, and hence more general classes of modified gravity need to be considered.