Reconstructing the boundary of AdS from an infrared defect

Cesar Arias

doi:10.1103/PhysRevD.108.126005

paper

Reconstructing the boundary of AdS from an infrared defect

arXiv:2307.02771 · doi:10.1103/PhysRevD.108.126005

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, $Σ^{d}$ : 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 $Z_{n}$ -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 $Σ$ is a 2-manifold of fixed positive curvature, and show that its $n \to \infty$ limit reproduces the central charge of Brown and Henneaux.

arXiv comment~30 pages, several figures and diagrams. V2: typos corrected, references added. Final, published version

Reconstructing the boundary of AdS from an infrared defect

Abstract

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