Reconstructing the boundary of AdS from an infrared defect

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.