Supertubes in Bubbling Backgrounds: Born-Infeld Meets Supergravity

TL;DR

This work shows that two-charge supertubes embedded in generic three-charge, three-dipole backgrounds are described consistently by both Born-Infeld probes and fully back-reacted six-dimensional supergravity, with the probe results reproducing the back-reacted smooth solutions in the D1-D5 frame. The authors establish entropy enhancement as a robust phenomenon arising from dipole interactions, demonstrating that local (effective) charges can be arbitrarily large and that entropy can approach black-hole-like scales for suitably shaped fluctuations. They map between multiple duality frames, clarify the role of Gibbons-Hawking patches in defining charges, and prove that the E$_{7(7)}$ quartic invariant governing four-dimensional entropy remains patch-independent, tying these microstate geometries to D1-D5 CFT states via AdS$_3$×S$^3$ decoupling. The results strengthen the case for infinite-parameter, smooth microstate geometries that reproduce black hole entropy and provide a concrete framework for holographic microstate counting, while highlighting subtle issues in certain mergers (ν ≠ -1) that warrant future fully back-reacted analyses.

Abstract

We discuss two ways in which one can study two-charge supertubes as components of generic three-charge, three-dipole charge supergravity solutions. The first is using the Born-Infeld action of the supertubes, and the second is via the complete supergravity solution. Even though the Born-Infeld description is only a probe approximation, we find that it gives exactly the same essential physics as the complete supergravity solution. Since supertubes can depend on arbitrary functions, our analysis strengthens the evidence for the existence of three-charge black-hole microstate geometries that depend on an infinite set of parameters, and sets the stage for the computation of the entropy of these backgrounds. We examine numerous other aspects of supertubes in three-charge, three-dipole charge supergravity backgrounds, including chronology protection during mergers, the contribution of supertubes to the charges and angular momenta, and the enhancement of their entropy. In particular, we find that entropy enhancement affects supertube fluctuations both along the internal and the spacetime directions, and we prove that the charges that give the enhanced entropy can be much larger than the asymptotic charges of the solution. We also re-examine the embedding of five-dimensional black rings in Taub-NUT, and show that in different coordinate patches a ring can correspond to different four-dimensional black holes. Last, but not least, we show that all the three-charge black hole microstate geometries constructed so far can be embedded in AdS_3 x S^3, and hence can be related to states of the D1-D5 CFT.

Figures (2)

• Figure 1: Different black ring and supertube configurations for different values of the supertube charges. In the first picture, the charges of the tube are too small, and hence the tube it is too small, and passes inside the ring. In the second one, the tube is too large and passes on the outside of the ring. In the third picture, the size of the tube is in the correct range for the merger to be possible. The angle $\alpha$ of the merger depends on the tube charges according to (\ref{['crudemerger']}).
• Figure 2: The black ring (in blue) with supertubes (in green) at various positions in the $\mathbb{R}^3$ base of the Gibbons-Hawking space. The black ring is point-like but the tube is point-like only if it lies on the axis $x=\pm1$. Otherwise, it winds $\nu+1$ times the $\phi$ circle. On the left, the Dirac string starts from the ring and extends to infinity. On the right, the Dirac string extends between the center of the space and the ring location.