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

TL;DR

<3-5 sentence high-level summary>We address how supersymmetric magnetic branes in AdS gauged supergravities can interpolate between near-horizon AdS$_{D-2}\times\Omega^2$ geometries and AdS$_D$-type asymptotics, deriving first-order flow equations from a superpotential. The analysis reveals two main solution branches: (i) smooth flows from AdS$_{D-2}\times\Omega^2$ in the IR to AdS$_D$ in the UV with Minkowski$_{D-3}\times\Omega^2$ boundaries, and (ii) stationary AdS$_{D-2}\times\Omega^2$ configurations that lie at modulus-space inflection points and can be singular in the small-distance limit. The results unify single-, two-, three-, and four-charge sectors across $D=4$–$7$, provide explicit domain-wall and brane solutions, and yield explicit uplifts to M-/string-theory backgrounds, offering holographic realizations of numerous RG flows between diverse CFTs. The work highlights the role of boundary compactification and flux constraints in shaping AdS/CFT realizations across dimensions.

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 Ω^2 (where Ω^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 Ω^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 Ω^2 but singular at small distance. This implies that the stationary AdS_{D-2}\times Ω^2 solutions typically lie on the inflection points of the modulus space.

Figures (9)

• Figure 1: $e^u$ (blue), $e^{v}$ (red) and $\phi$ (green) for a smooth solution that runs from AdS$_5\times H^2$ at the horizon to an AdS$_7$-type geometry in the asymptotic region.
• Figure 2: Plots of $e^u$ (blue), $e^{v}$ (red), $e^{\phi_1/\sqrt2}$ (green) and $e^{\phi_2/\sqrt{10}}$ (purple) in a smooth solution that runs from AdS$_{{ (5)}}\times H^2$ at the horizon to the AdS$_7$-type geometry in the asymptotic region. Note that the two scalar curves are almost identical on this scale. $m_1=16, m_2=6$, $g=1$, and $c=-0.1$.
• Figure 3: $e^u$ (blue), $e^{v}$ (red), $e^{\phi_1/\sqrt2}$ (green) and $e^{\phi_2/\sqrt{10}}$ (purple) for a smooth solution that runs from AdS$_{{ (5)}}\times S^2$ at horizon to the AdS$_7$-type geometry in the asymptotic region. $m_1=5, m_2=-3$, $g=1$, and $c=-0.2$.
• Figure 4: $e^u$ (blue), $e^{v}$ (red), $e^{\phi_1/\sqrt2}$ (green) and $e^{\phi_2/\sqrt{8}}$ (purple) for a smooth solution running from AdS$_4\times H^2$ at the horizon to an asymptotic AdS$_7$-type geometry. $m_1=5, m_2=-3$, $g=1$, and $c=-0.05$.
• Figure 5: $e^u$ (blue), $e^{v}$ (red), $e^{\phi_1/\sqrt2}$ (green) and $e^{\phi_2/\sqrt{8}}$ (purple) for a smooth solution running from AdS$_4\times S^2$ at the horizon to an asymptotic AdS$_6$-type geometry. $m_1=7, m_2=-5$, $g=1$, and $c=-0.2$.