The structure of BPS equations for ambi-polar microstate geometries

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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 AdS 3 ×S 2 5-dimensional superstrata have been produced, giving microstate geometries of black strings in 5 dimensions. Our construction produces asymptotically AdS 2 × 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 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-Kähler bases to produce prepotentials for the superstrata fluxes in 5 dimensions and uplift them to apply in 6 dimensions as well.

Section: Discussion Conclusion and Outlookmentioning

confidence: 95%

“…In [27] it was shown that in 5-dimensions the Θ (I) can be derived from harmonic functions on the GH base known as prepotentials Φ (I) . The construction is…”

Section: Prepotentials In 5-dimensionsmentioning

confidence: 99%

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

Walker

2019

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“…These solutions are completely regular for any choice of F (see Section 3.4.1); we also do not expect the existence of CTC's for any F . The angular momenta of the solution are: 35) and the momentum charge Q P is:…”

Section: A1 Solutions With Functions Of ξmentioning

confidence: 99%

Holomorphic waves of black hole microstructure

Heidmann

Mayerson

Walker

et al. 2020

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101

We obtain the largest families constructed to date of 1 8 -BPS solutions of type IIB supergravity. They have the same charges and mass as supersymmetric D1-D5-P black holes, but they cap off smoothly with no horizon. Their construction relies on the structure of superstratum states, but allows the momentum wave to have an arbitrary shape. Each family is based on an arbitrary holomorphic function of one variable. More broadly, we show that the most general solution is described by two arbitrary holomorphic functions of three variables. After exhibiting several new families of such "holomorphic superstrata," we reformulate the BPS backgrounds and equations in holomorphic form and show how this simplifies their structure. The holomorphic formulation is thus both a fundamental part of superstrata as well as an effective tool for their construction. In addition, we demonstrate that holomorphy provides a powerful tool in establishing the smoothness of our solutions without constraining the underlying functions. We also exhibit new families of solutions in which the momentum waves of the superstrata are highly localized at infinity but diffuse and spread into the infra-red limit in the core of the superstratum. Our work also leads to some results that can be tested within the dual CFT.

“…If we solve the zeroth layer, the remaining two layers can be written as linear differential equations on B. In practice, in most of the explicit superstratum solutions in the literature, it is assumed that the B is flat R 4 or a Gibbons-Hawking space [43,71,72], and that β is independent of v.…”

Section: The Zeroth Layermentioning

confidence: 99%

Counting superstrata

Shigemori

2019

We give a survey of the present status of the microstate geometries called superstrata. Superstrata are smooth, horizonless solutions of six-dimensional supergravity that represent some of the microstates of the D1-D5-P black hole in string theory. They are the most general microstate geometries of that sort whose CFT dual states are identified. After reviewing relevant features of the dual CFT, we discuss the construction of superstratum solutions in supergravity, based on the linear structure of the BPS equations. We also review some of recent work on generalizations of superstrata and physical properties of superstrata. Although the number of superstrata constructed so far is not enough to account for the black-hole entropy, they give us valuable insights into the microscopic physics of black holes.where J 3 0 is a generator of SU (2) L ∈ SO(4) coming from the rotational symmetry in the directions transverse to the D-branes.3 The CFT dual states of superstrata based on the five-dimensional multi-center solutions with two centers