Bulk Duals for Generic Static, Scale-Invariant Holographic CFT States

TL;DR

This paper explores new bulk dual geometries in holography for generic static, scale-invariant CFT states, extending beyond the symmetric near-horizon geometries, and provides numerical examples for gravity and gauge fields.

Contribution

It introduces bulk dual solutions for static, scale-invariant sources lacking enhanced symmetry, differing from traditional near-horizon geometries, with numerical examples in gravity and gauge fields.

Findings

Bulk duals with null singularities instead of extremal horizons.

Numerical solutions for pure gravity and abelian gauge fields.

Extended the class of known holographic duals for scale-invariant states.

Abstract

Near horizon geometries have been widely studied, and have found many applications. Certain static, near horizon geometries are now understood to be bulk duals to CFTs with static scale-invariant sources under the AdS/CFT correspondence. However, static near-horizon geometries aren't just scale-invariant, they have extra `enhanced' symmetry. This means that they can only be the bulk duals for a special class of static, scale-invariant sources that share this enhanced symmetry. The purpose of this paper is to consider bulk duals for more generic static, scale-invariant sources, without this extra symmetry. These solutions are quite different to near-horizon geometries. In place of the extremal horizon they have a null singularity. We find specific examples of such bulk geometries numerically for the cases of pure gravity, and for an abelian gauge field.