Magnetic and electric AdS solutions in string- and M-theory

TL;DR

The paper analyzes the stability of magnetic AdS3×R2 solutions in D=5 SO(6) gauged supergravity and constructs analogous magnetic AdS2×R2 solutions in D=4 SO(8) gauged supergravity, including supersymmetric cases. It identifies extensive instabilities—spatially modulated neutral scalars, charged scalars and vectors, and mixed modes—limiting stable regions to narrow SUSY-boundary loci and implying rich phase structures with holographic superconducting transitions. It further develops supersymmetric domain walls connecting AdS5/AdS4 in the UV to IR AdS3×R2 or AdS2×R2, describing stable zero-temperature ground states for the dual CFTs, and it extends the analysis to electric AdS2×R2 and AdS2×R3 solutions via dualities, highlighting non-supersymmetric stability challenges. The work provides comprehensive top-down (SUGRA) constructions with explicit domain-wall solutions and stability maps, offering holographic descriptions of quantum critical ground states in strongly coupled field theories under magnetic and electric fields and their uplifts to type IIB/I supergravity frameworks.

Abstract

The stability properties of a family of magnetic $AdS_{3}\times \mathbb{R}^{2}$ solutions of D=5, SO(6) gauged SUGRA are investigated in more detail. We construct an analogous family of magnetic $AdS_{2}\times \mathbb{R}^{2}$ solutions of D=4, SO(8) gauged SUGRA, including a family of supersymmetric solutions, and also investigate their stability. We construct supersymmetric domain walls that interpolate between AdS_5 and an $AdS_3\times\mathbb{R}^2$ solution and also between AdS_4 and an $AdS_2\times\mathbb{R}^2$ solution which provide stable zero temperature ground states for the corresponding dual CFTs. We also construct new families of electric $AdS_{2}\times \mathbb{R}^{3}$ and $AdS_{2}\times \mathbb{R}^{2}$ solutions.

Figures (5)

• Figure 1: The moduli space of magnetic $AdS_3\times \mathbb{R}^2$ solutions. Any point in the $(f_1,f_2)$ plane, combined with a set of signs for the $q^i$, gives rise to an $AdS_3\times \mathbb{R}^2$ solution. The red lines correspond to the locus of solutions that can preserve supersymmetry, for particular choices of the signs. The dashed lines correspond to solutions that can be embedded into Romans' theory and the origin corresponds to solutions that can be embedded in minimal gauged supergravity.
• Figure 2: We have plotted $U^{\prime}$ (blue) $W^{\prime}$ (purple) and $\phi$ (green) as functions of $\rho$ for the superssuperymmetricymmetric domain wall solution interpolating between $AdS_{5}$ and $AdS_{3}\times\mathbb{R}^2$ that exists in Romans' theory.
• Figure 3: The shaded regions in the $(f_{1},f_{2})$ plane indicate $AdS_3\times\mathbb{R}^2$ solutions for which we find have identified one or more unstable modes in $SO(6)$ gauged supergravity. Panel (a) indicates spatially modulated instabilities of neutral scalar fields, discussed in section \ref{['nscal']}, panel (b) indicates instabilities of the charged scalar modes discussed in section \ref{['sec1p4']} and panel (c) indicates instabilities of charged vector fields discussed in section \ref{['mixedcharged']}. Not shown are additional instabilities of mixed charged scalars and vectors discussed in section \ref{['mixedcharged']} that appear in subsets of the blue region. The supersymmetric solutions lie on the red lines.
• Figure 4: The moduli space of supersymmetric magnetic $AdS_2\times \mathbb{R}^2$ solutions in the $f_1,f_2,f_3$ space.
• Figure 5: We have plotted $U^{\prime}$ (blue) $W^{\prime}$ (purple) and $\phi$ (green) as functions of $\rho$ for the $U(1)^{2}\times SU(3)$ invariant supersymmetric domain wall solution interpolating between $AdS_{4}$ and $AdS_{2}\times\mathbb{R}^2$.