Habemus Superstratum! A constructive proof of the existence of superstrata (1503.01463v1)

Abstract: We construct the first example of a superstratum: a class of smooth horizonless supergravity solutions that are parameterized by arbitrary continuous functions of (at least) two variables and have the same charges as the supersymmetric D1-D5-P black hole. We work in Type IIB string theory on T^4 or K3 and our solutions involve a subset of fields that can be described by a six-dimensional supergravity with two tensor multiplets. The solutions can thus be constructed using a linear structure, and we give an explicit recipe to start from a superposition of modes specified by an arbitrary function of two variables and impose regularity to obtain the full horizonless solutions in closed form. We also give the precise CFT description of these solutions and show that they are not dual to descendants of chiral primaries. They are thus much more general than all the known solutions whose CFT dual is precisely understood. Hence our construction represents a substantial step toward the ultimate goal of constructing the fully generic superstratum that can account for a finite fraction of the entropy of the three-charge black hole in the regime of parameters where the classical black hole solution exists.

• The paper constructs explicit superstrata examples, offering the first concrete proof of their existence as smooth black-hole microstate geometries.
• The paper demonstrates that these solutions retain the D1-D5-P charge profiles using detailed Fourier expansions and regularity conditions in a six-dimensional framework.
• The paper establishes a broad CFT correspondence for superstrata, advancing our understanding of black-hole entropy through horizonless, microstate configurations.

Overview of "Habemus Superstratum! A Constructive Proof of the Existence of Superstrata"

The paper, titled "Habemus Superstratum! A Constructive Proof of the Existence of Superstrata," presents a significant advancement in the understanding of black-hole microstate geometries. The research focuses on the theoretical construction and demonstration of superstrata within six-dimensional supergravity derived from Type IIB string theory. These configurations are smooth, horizonless solutions mimicking the charge distributions of supersymmetric D1-D5-P black holes and are characterized by arbitrary continuous functions of two variables.

Main Contributions

1. Construction of Superstrata: The authors provide the first explicit examples of superstrata, a class of solutions that had been previously conjectured but not explicitly constructed. These solutions are derived within a six-dimensional framework and involve intricate manipulations using the theory's linear structure.
2. Charge and Configuration: The paper explores the properties of superstrata having the same charge profiles as D1-D5-P black holes. This demonstrates the possibility of describing black-hole microstates through smooth, geometric configurations in string theory, potentially replacing the black-hole horizon.
3. CFT Description: An essential aspect of the paper involves the conformal field theory (CFT) duality, where superstrata solutions correspond to specific states in the D1-D5 CFT. The research shows that these states are broader and more general than previously known solutions linked to chiral primaries, enhancing our understanding of dual CFT descriptions.
4. Entropy and Microstate Geometry: The paper posits that these solutions might account for a substantial portion of the black-hole entropy due to their parametric form as functions of two variables. This contributes to the fuzzball conjecture, suggesting that black-hole entropy could fundamentally arise from horizonless microstate geometries.
5. Implications for Black-Hole Physics: The existence of superstrata supports the hypothesis that classical descriptions of black holes, particularly their horizons, might be emergent structures from a deeper, microstate-based framework. This work potentially provides the tools to count microstates that correspond to classical black-hole entropy.

Numerical and Technical Results

The paper is rich with technical results, focusing on:

• Detailed solutions to the first and second layers of BPS equations necessary to construct superstrata.
• Expansions involving Fourier coefficients representing functions of two variables.
• Regularity conditions to ensure non-singular configurations.

Theoretical and Practical Implications

The realization of superstrata within supergravity heralds a shift in our approach to understanding black-hole microstates and entropy. These solutions pave the way for more complex models that offer insights into the nature of spacetime and gravity in high-energy regimes. Practical implications include advancements in how quantum microstate geometries might replace horizons in black-hole models.

Future Developments

The paper highlights opportunities for future research, particularly in:

• Extending the solution framework to encompass more general configurations.
• Investigating the implications of superstrata in other compactifications, such as those involving $K3$.
• Exploring the potential for superstrata to provide a complete account of black-hole microstate entropy across various regimes.

In summary, this paper marks a pivotal point in the paper of microstate geometries by providing a concrete construction of superstrata and laying the foundation for future explorations into string theory's ability to describe complex gravitational phenomena.