Flow equation for the large $N$ scalar model and induced geometries

TL;DR

This paper demonstrates that a large N scalar model's induced metric, derived via gradient flow, universally describes Euclidean AdS space in both UV and IR limits, with the IR radius larger than the UV.

Contribution

It shows that the induced metric from a large N scalar model is finite, universal, and describes AdS geometry, independent of flow details, depending only on the renormalized mass.

Findings

Induced metric is finite and universal in the large N limit.

The metric describes Euclidean AdS space in UV and IR limits.

AdS radius is larger in the IR than in the UV.

Abstract

We study the proposal that a $d+1$ dimensional induced metric is constructed from a $d$ dimensional field theory using gradient flow. Applying the idea to the O($N$) $\varphi^4$ model and normalizing the flow field, we have shown in the large $N$ limit that the induced metric is finite and universal in the sense that it does not depend on the details of the flow equation and the original field theory except for the renormalized mass, which is the only relevant quantity in this limit. We have found that the induced metric describes Euclidean Anti-de-Sitter (AdS) space in both ultra-violet (UV) and infra-red (IR) limits of the flow direction, where the radius of the AdS is bigger in the IR than in the UV.