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

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($N$) ${\phi }^4$ 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.

21 pages, 2 figures. We dedicate this work to the memory of Peter Hasenfratz. The revised version for the publication of PTEP

References in corpus (8)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Locally smeared operator product expansions in scalar field theory
• Future applications of the Yang-Mills gradient flow in lattice QCD
• Renormalizability of the gradient flow in the 2D $O(N)$ non-linear sigma model
• Gradient Flow of O(N) nonlinear sigma model at large N
• Proof of the renormalizability of the gradient flow
• Renormalisation of the energy-momentum tensor in scalar field theory using the Wilson flow
• Encoding field theories into gravities