Bubbling AdS space and 1/2 BPS geometries

TL;DR

This paper classifies all 1/2 BPS geometries in AdS spaces, linking smooth supergravity solutions to free fermion droplets, and explores their implications for dual field theories, geometric transitions, and compactifications.

Contribution

It provides a comprehensive classification of 1/2 BPS geometries in AdS spaces, connecting droplet configurations to smooth supergravity solutions and dual field theories.

Findings

Explicit solutions for 1/2 BPS geometries in AdS and plane wave backgrounds.

Identification of droplet topologies with geometry topology.

Realization of geometric transitions between branes and fluxes.

Abstract

We consider all 1/2 BPS excitations of $AdS \times S$ configurations in both type IIB string theory and M-theory. In the dual field theories these excitations are described by free fermions. Configurations which are dual to arbitrary droplets of free fermions in phase space correspond to smooth geometries with no horizons. In fact, the ten dimensional geometry contains a special two dimensional plane which can be identified with the phase space of the free fermion system. The topology of the resulting geometries depends only on the topology of the collection of droplets on this plane. These solutions also give a very explicit realization of the geometric transitions between branes and fluxes. We also describe all 1/2 BPS excitations of plane wave geometries. The problem of finding the explicit geometries is reduced to solving a Laplace (or Toda) equation with simple boundary conditions. We present a large class of explicit solutions. In addition, we are led to a rather general class of $AdS_5$ compactifications of M-theory preserving ${\cal N} =2$ superconformal symmetry. We also find smooth geometries that correspond to various vacua of the maximally supersymmetric mass-deformed M2 brane theory. Finally, we present a smooth 1/2 BPS solution of seven dimensional gauged supergravity corresponding to a condensate of one of the charged scalars.