# D1-D5-P superstrata in 5 and 6 dimensions: separable wave equations and prepotentials

## TL;DR

This paper constructs new superstrata geometries in 5 and 6 dimensions, revealing separable wave equations and prepotentials, and extends understanding of microstate geometries for black strings and black holes.

## Contribution

It introduces the most general single-mode superstrata in 5D with ambipolar bases, including new asymptotic geometries and mathematical structures like prepotentials.

## Key findings

- Constructed superstrata with asymptotic AdS2×S3 geometries.
- Discovered superstrata with separable wave equations in 5 and 6 dimensions.
- Identified a Z2 symmetry relating 6D superstrata when reduced to 5D.

## Abstract

We construct the most general single-mode superstrata in 5 dimensions with ambipolar, two centered Gibbons Hawking bases, via dimensional reduction of superstrata in 6 dimensions. Previously, asymptotically $\text{AdS}_{3}\times \mathbb{S}^{2}$ 5-dimensional superstrata have been produced, giving microstate geometries of black strings in 5 dimensions. Our construction produces asymptotically $\text{AdS}_{2}\times \mathbb{S}^{3}$ geometries as well, the first instances of superstrata describing the microstate geometries of black holes in 5 dimensions. New examples of superstrata with separable massless wave equations in both 5 and 6 dimensions are uncovered. A $\mathbb{Z}_{2}$ symmetry which identifies distinct 6-dimensional superstrata when reduced to 5 dimensions is found. Finally we use the mathematical structure of the underlying hyper-K\"{a}hler bases to produce prepotentials for the superstrata fluxes in 5 dimensions and uplift them to apply in 6 dimensions as well.