Holographic CFTs on AdSd × Sn and conformal defects

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 AdSd × Sn. Their only dimensionless parameter is the ratio of radii of curvatures of AdSd and Sn. The same solutions may also be dual to (d − 1)-dimensional conformal defects in holographic QFTd+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 AdSd+n+1 and another to AdSd × AdSn+1. For the regular solutions, we compute the on-shell action as a function of the relevant parameters.