Interpolating from AdS_(D-2) X S^2 to AdS_D

TL;DR

This paper constructs smooth supergravity solutions that interpolate between lower-dimensional AdS spaces times a sphere or hyperbolic space and higher-dimensional AdS geometries, revealing insights into RG flows of superconformal theories.

Contribution

It introduces a class of interpolating supersymmetric solutions in AdS gauged supergravity for dimensions 4 to 7, connecting different AdS geometries and their boundary field theories.

Findings

Smooth interpolating solutions between AdS_{D-2}×S^2/H^2 and AdS_D

Solutions support spontaneous boundary compactification

Existence of singular solutions at small distances

Abstract

We investigate a large class of supersymmetric magnetic brane solutions supported by U(1) gauge fields in AdS gauged supergravities. We obtain first-order equations in terms of a superpotential. In particular, we find systems which interpolate between AdS_{D-2}\times \Omega^2 (where \Omega^2=S^2 or H^2) in the horizon and AdS_D-type geometry in the asymptotic region, for 4\le D\le 7. The boundary geometry of the AdS_D-type metric is Minkowski_{D-3}\times \Omega^2. This provides smooth supergravity solutions for which the boundary of the AdS spacetime compactifies spontaneously. These solutions indicate the existence of a large class of superconformal field theories in diverse dimensions whose renormalization group flow runs from the UV to the IR fixed point. We show that the same set of first-order equations also admits solutions which are asymptotically AdS_{D-2}\times \Omega^2 but singular at small distance. This implies that the stationary AdS_{D-2}\times \Omega^2 solutions typically lie on the inflection points of the modulus space.