Conical defects and holography in topological AdS gravity

TL;DR

This paper explores the role of codimension-even conical defects in topological AdS gravity, establishing a holographic duality with brane solutions and analyzing their contributions to the Lovelock scalar and Weyl anomaly.

Contribution

It introduces a novel holographic duality between defect partition functions and brane on-shell actions in Lovelock-Chern-Simons gravity, with explicit calculations and geometric insights.

Findings

Defects contribute delta functions to the Lovelock scalar.

Holographic duality matches defect partition functions with brane actions.

Geometry reduces to a foliation of Euclidean AdS space for zero tension.

Abstract

We study codimension-even conical defects that contain a deficit solid angle around each point along the defect. We show that they lead to a delta function contribution to the Lovelock scalar and we compute the contribution by two methods. We then show that these codimension-even defects appear as Euclidean brane solutions in higher dimensional topological AdS gravity which is Lovelock-Chern-Simons gravity without torsion. The theory possesses a holographic Weyl anomaly that is purely of type-A and proportional to the Lovelock scalar. Using the formula for the defect contribution, we prove a holographic duality between codimension-even defect partition functions and codimension-even brane on-shell actions in Euclidean signature. More specifically, we find that the logarithmic divergences match, because the Lovelock-Chern-Simons action localizes on the brane exactly. We demonstrate the duality explicitly for a spherical defect on the boundary which extends as a codimension-even hyperbolic brane into the bulk. For vanishing brane tension, the geometry is a foliation of Euclidean AdS space that provides a one-parameter generalization of AdS-Rindler space.