Supersymmetric Charged Clouds in AdS_5

TL;DR

This work develops a comprehensive framework for supersymmetric holographic flows in AdS_5 with background gauge fields corresponding to boundary chemical potentials. By performing a consistent truncation to N=2 gauged supergravity and deriving a full first-order flow system driven by a superpotential W, the authors uncover a new smooth flow between two global AdS_5 vacua with differing radii and electrostatic potentials, mediated by a charged hypermultiplet cloud. They also analyze charged black-hole-like and naked-singularity solutions, including constant-scalar STU configurations and non-supersymmetric AdS_5 black holes, and discuss their ten-dimensional uplifts as giant gravitons. The results illuminate how chemical potentials reshape holographic RG flows, offer new stable backgrounds for AdS/CMT explorations, and suggest rich avenues for future work, such as incorporating magnetic fields and extending to M-theory or almost-BPS constructions. Overall, the paper provides new exact BPS backgrounds and domain-wall solutions with charged clouds, advancing the holographic understanding of AdS black holes and condensed-matter-like phases in strongly coupled gauge theories.

Abstract

We consider supersymmetric holographic flows that involve background gauge fields dual to chemical potentials in the boundary field theory. We use a consistent truncation of gauged N=8 supergravity in five dimensions and we give a complete analysis of the supersymmetry conditions for a large family of flows. We examine how the well-known supersymmetric flow between two fixed points is modified by the presence of the chemical potentials and this yields a new, completely smooth, solution that interpolates between two global AdS spaces of different radii and with different values of the chemical potential. We also examine some black-hole-like singular flows and a new non-supersymmetric black hole solution. We comment on the interpretation of our new solutions in terms of giant gravitons and discuss the implications of our work for finding black-hole solutions in AdS geometries.

Figures (4)

• Figure 1: The profiles of the scalar functions $\alpha(A)$, $\chi(A)$ obtained by solving equation (\ref{['steep']}) and the metric function $f(A)$ obtained by solving equation (\ref{['metflow']}). For clarity, we have plotted the functions $\alpha(A)$, $\chi(A)$ and $(f(A)-1)/10$.
• Figure 2: The black dashed lines are the functions given in equation (\ref{['exactalpha']})--(\ref{['exactf']}). Clearly they resemble the numerical solutions very closely.
• Figure 3: The profiles of the scalar functions $\alpha(A)$, $\chi(A)$ obtained by solving the BPS flow equations in Poincaré patch. We have also set $c = 1$, $g = 1$. They do interpolate between the UV and the IR fixed points.
• Figure 4: The profiles of the scalar functions $\alpha(A)$, $\chi(A)$ and $\Phi(A) \equiv \Phi_2(A)$ obtained by solving the BPS flow equations in global coordinates. For numerical purpose we have set $c = 1$, $g = 1$ and $a = 1$. Note that all fields vary within the same region in $A$-space and that $\Phi$ is diverging exponentially and $f$ is determined by \ref{['Phians1']}.