Holographic CFTs on $AdS_d\times S^n$ and conformal defects

TL;DR

This paper classifies and analyzes solutions of Einstein gravity with negative curvature that are dual to certain holographic conformal field theories on curved spaces and conformal defects, revealing unique regular solutions and their properties.

Contribution

It provides a comprehensive classification of solutions dual to holographic CFTs on $AdS_d\times S^n$ and conformal defects, including analytical and numerical analysis of regular and singular solutions.

Findings

No solutions with two boundaries along the holographic direction.

Only two regular solutions: one diffeomorphic to $AdS_{d+n+1}$ and another to $AdS_d\times AdS_{n+1}$.

Computed on-shell action for regular solutions as a function of parameters.

Abstract

We consider ($d+n+1$)-dimensional solutions of Einstein gravity with constant negative curvature. Regular solutions of this type are expected to be dual to the ground states of ($d+n$)-dimensional holographic CFTs on $AdS_d\times S^n$. Their only dimensionless parameter is the ratio of radii of curvatures of $AdS_d$ and $S^n$. The same solutions may also be dual to $(d-1)$-dimensional conformal defects in holographic QFT$_{d+n}$. We solve the gravity equations with an associated conifold ansatz, and we classify all solutions both singular and regular by a combination of analytical and numerical techniques. There are no solutions, regular or singular, with two boundaries along the holographic direction. Out of the infinite class of regular solutions, only one is diffeomorphic to $AdS_{d+n+1}$ and another to $AdS_d\times AdS_{n+1}$. For the regular solutions, we compute the on-shell action as a function of the relevant parameters.