Holographic CFTs on $Ad{S}_d\times S^n$ 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 $Ad{S}_d\times S^n$. Their only dimensionless parameter is the ratio of radii of curvatures of $Ad{S}_d$ 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 $Ad{S}_{d+n+1}$ and another to $Ad{S}_d\times Ad{S}_{n+1}$. For the regular solutions, we compute the on-shell action as a function of the relevant parameters.

75 pages, 23 figures

References in corpus (8)

• Holographic c-theorems in arbitrary dimensions
• Seeing a c-theorem with holography
• Exact half-BPS Type IIB interface solutions I: Local solution and supersymmetric Janus
• The No-Boundary Measure of the Universe
• Ten-dimensional supersymmetric Janus solutions
• Euclidean Wormholes and Holography
• Defects in scalar field theories, RG flows and Dimensional Disentangling
• Holographic QFTs on AdS${}_d$, wormholes and holographic interfaces