Bubbling AdS3
Dario Martelli, Jose F. Morales
TL;DR
The paper extends the LLM bubbling program to ${AdS_3}\times S^3$ in six-dimensional supergravity, showing that half-BPS deformations can be described by droplet configurations on a two-dimensional plane. While a rectangular $T^2$ freezes the system with a nonlinear link between the bubbling functions, tilting the torus restores a linear bubbling structure analogous to LLM, now encoded by a pair of harmonic functions and their boundary data. The analysis connects minimal D=6 supergravity to D1D5 geometries, and, with a tensor multiplet, to giant gravitons and broader D1D5 microstate solutions, all captured by droplet boundaries. Overall, bubbling in AdS$_3$ is established as a geometric translation of chiral primaries in the dual 2D CFT, with a clear DBI-like boundary description driving the microstate construction.
Abstract
In the light of the recent Lin, Lunin, Maldacena (LLM) results we investigate 1/2-BPS geometries in minimal (and next-to minimal) supergravity in D=6 dimensions. In the case of minimal supergravity, solutions are given by fibrations of a two-torus T^2 specified by two harmonic functions. For a rectangular torus the two functions are related by a non-linear equation with rare solutions: AdS_3x S^3, the pp-wave and the multi-center string. ``Bubbling'', i.e. superpositions of droplets, is accommodated by allowing the complex structure of the T^2 to vary over the base. The analysis is repeated in the presence of a tensor multiplet and similar conclusions are reached with generic solutions describing D1D5 (or their dual fundamental string-momentum) systems. In this framework, the profile of the dual fundamental string-momentum system is identified with the boundaries of the droplets in a two-dimensional plane.