Bubbling AdS3

TL;DR

This paper explores 1/2-BPS geometries in six-dimensional supergravity, revealing how bubbling solutions correspond to droplet configurations and extending the analysis to systems involving tensor multiplets and D1D5 branes.

Contribution

It provides a detailed construction of bubbling geometries in minimal and next-to-minimal supergravity, linking droplet profiles to dual string-momentum systems.

Findings

Bubbling solutions are described by droplet superpositions with varying complex structures.

The analysis extends to D1D5 systems, connecting droplet boundaries to string-momentum profiles.

Rare solutions include AdS_3x S^3, pp-waves, and multi-center strings.

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.