Habemus Superstratum! A constructive proof of the existence of superstrata

TL;DR

Habemus Superstratum! delivers a constructive proof of the existence of superstrata by solving the six-dimensional supergravity equations in a linear, layer-structured framework and enforcing regularity to produce smooth horizonless D1-D5-P geometries parameterized by functions of two variables. The construction starts from a round two-charge supertube, adds left-moving momentum modes via a controlled solution-generating procedure, and then assembles a general first-layer solution into a fully non-linear second-layer geometry, yielding explicit $Z_4^{(k,m)}$-type modes and their corresponding $m{\Theta}_4$ contributions. The authors also map these geometries to explicit states in the D1-D5 CFT at the free orbifold point, showing that they are descendants of non-chiral primaries and thus extend beyond previously understood chiral-primary descendants. This work provides strong evidence that a substantial fraction of the three-charge black hole entropy can be captured by smooth microstate geometries and lays out a clear program toward a fully generic, twisted-sector superstratum with potential entropy counting in the dual CFT.

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.

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