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〉-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.
Highlights
The construction of superstrata [1] has proven to be a very important advance in the development of microstate geometries
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
Smoothness of the complete supergravity solution 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
Summary
The construction of superstrata [1] has proven to be a very important advance in the development of microstate geometries. Much of the focus has been on classes of “single-mode” superstrata that are dual to excitations of a single state of the form (1.1) Such geometries have the virtue of being relatively simple and yet exhibit an incredibly rich structure in terms of parallels with, and differences from, black holes. It became apparent that for the original classes of superstrata (qi = 0), regularity of completely general multi-mode excitations would place some further restrictions on the “leading” Fourier coefficients as well This would suggest a major deficiency in superstrata as duals of the CFT states. The supergravity leads to new holographically testable CFT predictions: interactions of the original superstratum states lead to excitations of light supercharged operators, and their expectation values are determined by the coiffuring constraints.
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