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Double, Double Supertube Bubble

Iosif Bena, Jan de Boer, Masaki Shigemori, Nicholas P. Warner

TL;DR

This work introduces superstrata, a novel class of completely smooth 1/8-BPS three-charge bound states that depend on functions of two variables and locally resemble 1/2-BPS objects. By double bubbling a D1–D5–P system, the authors construct a two-dimensional sheet embedded in the five-dimensional base, where each patch is 1/2-BPS with a shared 4-supersymmetry sector, enabling arbitrary two-variable embeddings. In the D1-D5-P frame these configurations yield horizonless microstate geometries that could substantially illuminate black-hole entropy in holographic contexts, potentially accounting for more entropy than traditional one-variable supertubes. The paper develops a projector-based framework to demonstrate the local existence of such configurations, sketches basis changes that clarify the supersymmetry structure, and outlines the path toward explicit supergravity realizations while acknowledging remaining theoretical challenges.

Abstract

We argue that there exists a new class of completely smooth 1/8-BPS, three-charge bound state configurations that depend upon arbitrary functions of two variables. These configurations are locally 1/2-BPS objects in that if they form an infinite flat sheet then they preserve 16 supersymmetries but even with arbitrary two-dimensional shape modes they still preserve 4 supersymmetries. They have three electric charges and can be thought of the result of two successive supertube transitions that involve adding two independent dipole moments and giving rise to the arbitrary two-dimensional shape modes. We further argue that in the D1-D5-P duality frame this construction will give rise to smooth, horizonless solutions, or microstate geometries. We expect these solutions to be extremely important in the semi-classical and holographic descriptions of black-hole entropy.

Double, Double Supertube Bubble

TL;DR

This work introduces superstrata, a novel class of completely smooth 1/8-BPS three-charge bound states that depend on functions of two variables and locally resemble 1/2-BPS objects. By double bubbling a D1–D5–P system, the authors construct a two-dimensional sheet embedded in the five-dimensional base, where each patch is 1/2-BPS with a shared 4-supersymmetry sector, enabling arbitrary two-variable embeddings. In the D1-D5-P frame these configurations yield horizonless microstate geometries that could substantially illuminate black-hole entropy in holographic contexts, potentially accounting for more entropy than traditional one-variable supertubes. The paper develops a projector-based framework to demonstrate the local existence of such configurations, sketches basis changes that clarify the supersymmetry structure, and outlines the path toward explicit supergravity realizations while acknowledging remaining theoretical challenges.

Abstract

We argue that there exists a new class of completely smooth 1/8-BPS, three-charge bound state configurations that depend upon arbitrary functions of two variables. These configurations are locally 1/2-BPS objects in that if they form an infinite flat sheet then they preserve 16 supersymmetries but even with arbitrary two-dimensional shape modes they still preserve 4 supersymmetries. They have three electric charges and can be thought of the result of two successive supertube transitions that involve adding two independent dipole moments and giving rise to the arbitrary two-dimensional shape modes. We further argue that in the D1-D5-P duality frame this construction will give rise to smooth, horizonless solutions, or microstate geometries. We expect these solutions to be extremely important in the semi-classical and holographic descriptions of black-hole entropy.

Paper Structure

This paper contains 23 sections, 93 equations, 5 figures.

Table of Contents

  1. Introduction
  2. The physical description of superstrata
  3. Supertube transitions
  4. Supersymmetries and supertubes in general
  5. A simple example: the F1--P system
  6. Bubbling the D1--D5 system
  7. Bubbling the D1--P and D5--P system
  8. Double Bubbling
  9. The transition to the three-charge supertube
  10. A basis change
  11. The double-bubbled superstratum
  12. Conclusions
  13. Detailed analysis of the projectors for double bubbling
  14. Supersymmetry algebra and projectors for branes
  15. The generic supertube transition
  16. ...and 8 more sections

Figures (5)

  • Figure 1: The D1-P or F1-P supertube profile and a typical local neighbourhood.
  • Figure 2: The double bubbling of the D1-D5-P system. There are two ways to obtain a superstratum : The D1 and P can fuse into a D1-P supertube spiral (red dotted line), and the D5 and P can fuse into a D5-P spiral (blue continuous line). The spirals can then fuse into a superstratum . Alternatively the D1-D5 can fuse into a D1-D5-KKM tube (violet straight supertube), which upon adding momentum can start shaking and become a superstratum .
  • Figure 3: The zoom-in near an F1-P supertube profile
  • Figure 4: Boosting and rotating to obtain the desired F1-P configuration
  • Figure 5: The straight D1-D5-P tube configuration.