# Superstratum Symbiosis

## TL;DR

This paper demonstrates how supercharged superstrata are essential for constructing the supergravity dual of generic superstratum states, showing their fluctuations, smoothness conditions, and implications for dual CFT three-point functions and scalar perturbations.

## Contribution

It introduces supercharged superstrata as a key component for the supergravity dual of generic superstratum states and explores their properties and implications.

## Key findings

- Supercharged superstrata complete the supergravity description of generic states.
- Superstrata fluctuate as functions of three variables, confirming their rich structure.
- Scalar wave analysis shows the mass gap depends on free moduli, affecting thermal behavior.

## Abstract

Superstrata are smooth horizonless microstate geometries for the supersymmetric D1-D5-P black hole in type IIB supergravity. In the CFT, 'superstratum states' are defined to be the component of the supergraviton gas that is obtained by breaking the CFT into '$|00\rangle$-strands' and acting on each strand with the 'small,' anomaly-free superconformal generators. We show that the recently-constructed supercharged superstrata represent a final and crucial component for the construction of the supergravity dual of a generic superstratum state and how the supergravity solution faithfully represents all the coherent superstratum states of the CFT. For the supergravity alone, this shows that generic superstrata do indeed fluctuate as functions of three independent variables. Smoothness of the complete supergravity solution also involves 'coiffuring constraints' at second-order in the fluctuations and we describe how these lead to new predictions for three-point functions in the dual CFT. We use a hybrid of the original and supercharged superstrata to construct families of single-mode superstrata that still have free moduli after one has fixed the asymptotic charges of the system. We also study scalar wave perturbations in a particular family of such solutions and show that the mass gap depends on the free moduli. This can have interesting implications for superstrata at non-zero temperature.