BPS Geometries and AdS Bubbles
Z. -W. Chong, H. Lu, C. N. Pope
TL;DR
This work extends the Lin-Lunin-Maldacena $1/2$-BPS AdS bubble solutions by incorporating additional gauge fields and scalars to generate AdS bubble generalisations of multi-charge AdS black holes across $D=7,5,4$ gauged supergravities (and a $D=6$ case). By constructing explicit ansatze with multiple charges and deriving the governing differential equations for the harmonic functions $H_i$, the authors obtain $1/4$-BPS seven-dimensional bubbles, $1/8$-BPS five- and four-dimensional bubbles, and a $1/4$-BPS six-dimensional bubble, with various special cases yielding higher fractions of supersymmetry. These solutions lift to M-theory or type IIB string theory through known Pauli sphere reductions, and in six dimensions they admit a lift to massive type IIA supergravity, broadening the catalog of supersymmetric AdS geometries and their holographic interpretations. Overall, the paper provides a unified framework for multi-charge AdS bubbles and highlights their connections to dual CFT droplet pictures via AdS/CFT.
Abstract
Recently, 1/2-BPS AdS bubble solutions have been obtained by Lin, Lunin and Maldacena, which correspond to Fermi droplets in phase space in the dual CFT picture. They can be thought of as generalisations of 1/2-BPS AdS black hole solutions in five or seven dimensional gauged supergravity. In this paper, we extend these solutions by invoking additional gauge fields and scalar fields in the supergravity Lagrangians, thereby obtaining AdS bubble generalisations of the previously-known multi-charge AdS black solutions of gauged supergravity. We also obtain analogous AdS bubble solutions in four-dimensional gauged supergravity. Our solutions generically preserve supersymmetry fractions 1/4, 1/8 and 1/8 in seven, five and four dimensions respectively. They can be lifted to M-theory or type IIB string theory, using previously known formulae for the consistent Pauli sphere reductions that yield the gauged supergravities. We also find similar solutions in six-dimensional gauged supergravity, and discuss their lift to the massive type IIA theory.