Reconstructing the boundary of AdS from an infrared defect

TL;DR

This paper proposes a novel way to reconstruct the boundary of an AdS space from a deep interior defect, suggesting an infrared field theory on a bulk orbifold defect that encodes boundary holography.

Contribution

It introduces the concept of reconstructing AdS boundary data from an interior defect and conjectures an associated infrared field theory that reproduces known boundary holographic results.

Findings

Computed a defect central charge matching Brown-Henneaux in the large n limit.

Established a dual perspective of the boundary as an interior defect.

Proposed a new geometric framework for holography involving orbifold defects.

Abstract

We argue that the boundary of an asymptotically anti-de Sitter (AdS) space of dimension $d+1$, say $M^{d+1}$, can be locally reconstructed from a codimension-two defect located in the deep interior of a negatively curved Einstein manifold $X^{d+2}$ of one higher dimension. This means that there exist two different ways of thinking about the same $d$-submanifold, $\Sigma^d$: either as a defect embedded in the interior of $X^{d+2}$, or as the boundary of $M^{d+1}$ in a certain zero radius limit. Based on this idea and other geometric and symmetry arguments, we propose the existence of an infrared field theory on a bulk $\mathbb Z_n$-orbifold defect, located in the deepest point of the interior of AdS$^{d+2}$. We further conjecture that such a theory gives rise to the holographic theory at the asymptotic boundary of AdS$^{d+1}$, in the limit where the orbifold parameter $n\to\infty$. As an example, we compute a defect central charge when $\Sigma$ is a 2-manifold of fixed positive curvature, and show that its $n\to\infty$ limit reproduces the central charge of Brown and Henneaux.