arXiv subjects

Nicholas P. Warner

Publications and source records attributed to Nicholas P. Warner.

At least 37 records · Page 2Linked to original sources

arXiv2021

Holomorphic Waves of Black Hole Microstructure

We obtain the largest families constructed to date of $\tfrac{1}{8}$-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.

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arXiv2021

The Great Escape: Tunneling out of Microstate Geometries

We compute the quasi-normal frequencies of scalars in asymptotically-flat microstate geometries that have the same charge as a D1-D5-P black hole, but whose long BTZ-like throat ends in a smooth cap. In general the wave equation is not separable, but we find a class of geometries in which the non-separable term is negligible and we can compute the quasi-normal frequencies using WKB methods. We argue that our results are a universal property of all microstate geometries with deeply-capped BTZ throats. These throats generate large redshifts, which lead to exceptionally-low-energy states with extremely long decay times, set by the central charge of the dual CFT to the power of twice the dimension of the operator dual to the mode. While these decay times are extremely long, we also argue that the energy decay is bounded, at large $t$, by $(log~t)^{-2}$ and is comparable with the behavior of ultracompact stars, as one should expect for microstate geometries.

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arXiv2021

Supersymmetry and Superstrata in Three Dimensions

We analyze the supersymmetry transformations of gauged $SO(4)$ supergravity coupled to extra hypermultiplets in three dimensions, and find large families of smooth BPS solutions that preserve four supersymmetries. These BPS solutions are part of the consistent truncation of some families of six-dimensional superstrata. From the three-dimensional perspective, these solutions give rise to "smoothly-capped BTZ" geometries. We show how the twisting of the spin connection, the holomorphy of the fields, and the Chern-Simons connections all play an essential role in the existence of these supersymmetric solutions. This paper also closes the circle on the consistent truncation of superstrata, showing precisely how every feature of the superstratum enters into the three-dimensional BPS structure.

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arXiv2021

Delaying the Inevitable: Tidal Disruption in Microstate Geometries

Microstate geometries in string theory replace the black-hole horizon with a smooth geometric "cap" at the horizon scale. In geometries constructed using superstratum technology, this cap has the somewhat surprising property that induces very large tidal deformations on infalling observers that are far away from it. We find that this large-distance amplification of the tidal effects is also present in horizonless microstate geometries constructed as bubbling solutions, but can be tamed by suitably arranging the bubbles to reduce the strength of some of the gravitational multipole moments. However, despite this taming, these tidal effects still become large at a significant distance from the microstructure. This result suggests that an observer will not fall unharmed into the structure replacing the black hole horizon.

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arXiv2021

Separability in Consistent Truncations

The separability of the Hamilton-Jacobi equation has a well-known connection to the existence of Killing vectors and rank-two Killing tensors. This paper combines this connection with the detailed knowledge of the compactification metrics of consistent truncations on spheres. The fact that both the inverse metric of such compactifications, as well as the rank-two Killing tensors can be written in terms of bilinears of Killing vectors on the underlying "round metric," enables us to perform a detailed analyses of the separability of the Hamilton-Jacobi equation for consistent truncations. We introduce the idea of a separating isometry and show that when a consistent truncation, without reduction gauge vectors, has such an isometry, then the Hamilton-Jacobi equation is always separable. When gauge vectors are present, the gauge group is required to be an abelian subgroup of the separating isometry to not impede separability. We classify the separating isometries for consistent truncations on spheres, $S^n$, for $n=2, \dots, 7$, and exhibit all the corresponding Killing tensors. These results may be of practical use in both identifying when supergravity solutions belong to consistent truncations and generating separable solutions amenable to scalar probe calculations. Finally, while our primary focus is the Hamilton-Jacobi equation, we also make some remarks about separability of the wave equation.

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arXiv2021

The Harder They Fall, the Bigger They Become: Tidal Trapping of Strings by Microstate Geometries

We consider the fate of a massless (or ultra-relativistic massive) string probe propagating down the BTZ-like throat of a microstate geometry in the D1-D5 system. Far down the throat, the probe encounters large tidal forces that stretch and excite the string. The excitations are limited by the very short transit time through the region of large tidal force, leading to a controlled approximation to tidal stretching. We show that the amount of stretching is proportional to the incident energy, and that it robs the probe of the kinetic energy it would need to travel back up the throat. As a consequence, the probe is effectively trapped far down the throat and, through repeated return passes, scrambles into the ensemble of nearby microstates. We propose that this tidal trapping may lead to weak gravitational echoes.

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arXiv2020

Microstate Geometries from Gauged Supergravity in Three Dimensions

The most detailed constructions of microstate geometries, and particularly of superstrata, are done using $\mathcal{N} = (1,0)$ supergravity coupled to two anti-self-dual tensor multiplets in six dimensions. We show that an important sub-sector of this theory has a consistent truncation to a particular gauged supergravity in three dimensions. Our consistent truncation is closely related to those recently laid out by Samtleben and Sarioglu (arXiv:1907.08413 [hep-th]), which enables us to develop complete uplift formulae from the three-dimensional theory to six dimensions. We also find a new family of multi-mode superstrata, indexed by two arbitrary holomorphic functions of one complex variable, that live within our consistent truncation and use this family to provide extensive tests of our consistent truncation. We discuss some of the future applications of having an intrinsically three-dimensional formulation of a significant class of microstate geometries.

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arXiv2020

Brane-Jet Instabilities

With one exception, all known non-supersymmetric AdS$_4$ and AdS$_5$ vacua of gauged maximal supergravities that descend from string and M theory have been shown to have modes with mass below the BF bound. The remaining non-supersymmetric AdS solution is perturbatively stable within gauged maximal supergravity, and hence appears to contradict recent conjectures about the AdS stability based on the weak gravity conjecture. We show that this solution is actually unstable by exhibiting a new decay channel, which is only visible when the solution is uplifted to eleven dimensions. In particular, M2 brane probes at generic locations inside the internal manifold are attracted to the Poincaré horizon, only to be expelled as "brane jets" along certain directions of the internal manifold. Such instabilities can arise in any non-supersymmetric AdS vacuum in any dimension. When a brane-jet instability is present, the force that expels the branes is the same as the force felt by a probe brane whose mass is less than its charge.

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arXiv2019

Lectures on Microstate Geometries

These are notes for some introductory lectures about microstate geometries and their construction. The first lecture considers BPS black holes in four dimensions as a way to introduce what one should expect from the BPS equations. The second lecture discusses the "no solitons without topology" theorem. The subsequent lectures move on to the construction and properties of bubbled microstate geometries in five dimensions. Since these are graduate lectures, they involve a strongly computational narrative intended to build some proficiency and understanding of supersymmetric solitons in five-dimensions. The narrative also regularly "plays tourist" pointing to specific features that are more general or have broader impact. The last sections contain brief comments on the larger setting of microstate geometries and describe some of the more recent developments. These lectures were given as a mini-course at the IPhT, Saclay in May, 2019.

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arXiv2019

Thermal Decay without Information Loss in Horizonless Microstate Geometries

We develop a new hybrid WKB technique to compute boundary-to-boundary scalar Green functions in asymptotically-AdS backgrounds in which the scalar wave equation is separable and is explicitly solvable in the asymptotic region. We apply this technique to a family of six-dimensional $\frac{1}{8}$-BPS asymptotically AdS$_3\,\times\,$S$^3$ horizonless geometries that have the same charges and angular momenta as a D1-D5-P black hole with a large horizon area. At large and intermediate distances, these geometries very closely approximate the extremal-BTZ$\,\times\,$S$^3$ geometry of the black hole, but instead of having an event horizon, these geometries have a smooth highly-redshifted global-AdS$_3\,\times\,$S$^3$ cap in the IR. We show that the response function of a scalar probe, in momentum space, is essentially given by the pole structure of the highly-redshifted global-AdS$_3$ modulated by the BTZ response function. In position space, this translates into a sharp exponential black-hole-like decay for times shorter than $N_1 N_5$, followed by the emergence of evenly spaced "echoes from the cap," with period $\sim N_1 N_5$. Our result shows that horizonless microstate geometries can have the same thermal decay as black holes without the associated information loss.

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arXiv2019

Superstratum Symbiosis

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.

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arXiv2018

Early Scrambling and Capped BTZ Geometries

Geodesic probes in certain horizonless microstate geometries experience extreme tidal forces long before reaching the region where these geometries differ significantly from the extremal BTZ black hole. The purpose of this paper is to show that this behavior is a universal feature of all geometries that have a long BTZ throat that terminates in a cap, regardless of the details of this cap. Hence, incoming probes will scramble into the microstate structure before they encounter the region where the charges of the solution are sourced, and the reason for this premature scrambling is the amplification of tiny geometrical deviations by the relativistic speeds of the probes. To illustrate the phenomenon, we construct a new family of smooth horizonless superstratum microstate geometries, dual to D1-D5 CFT states whose momentum charge is carried by excitations on CFT strands of length $k$. We also show that, in the large-$k$ limit, these new superstrata resemble a blackened supertube solution everywhere except in the near-supertube region. Thus they resolve the singularity caused by the naive back-reaction of modes with non-linear instabilities near evanescent ergosurfaces.

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arXiv2018

The Structure of BPS Equations for Ambi-polar Microstate Geometries

Ambi-polar metrics, defined so as to allow the signature to change from +4 to -4 across hypersurfaces, are a mainstay in the construction of BPS microstate geometries. This paper elucidates the cohomology of these spaces so as to simplify greatly the construction of infinite families of fluctuating harmonic magnetic fluxes. It is argued that such fluxes should come from scalar, harmonic pre-potentials whose source loci are holomorphic divisors. This insight is obtained by exploring the Kahler structure of ambi-polar Gibbons-Hawking spaces and it is shown that differentiating the pre-potentials with respect to Kahler moduli yields solutions to the BPS equations for the electric potentials sourced by the magnetic fluxes. This suggests that harmonic analysis on ambi-polar spaces has a novel, and an extremely rich structure, that is deeply intertwined with the BPS equations. We illustrate our results using a family of two-centered solutions.

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arXiv2017

BPS equations and Non-trivial Compactifications

We consider the problem of finding exact, eleven-dimensional, BPS supergravity solutions in which the compactification involves a non-trivial Calabi-Yau manifold, ${\cal Y}$, as opposed to simply a $T^6$. Since there are no explicitly-known metrics on non-trivial, compact Calabi-Yau manifolds, we use a non-compact "local model" and take the compactification manifold to be ${\cal Y} = {\cal M}_{GH} \times T^2$ where ${\cal M}_{GH}$ is a hyper-Kähler, Gibbons-Hawking ALE space. We focus on backgrounds with three electric charges in five dimensions and find exact families of solutions to the BPS equations that have the same four supersymmetries as the three-charge black hole. Our exact solution to the BPS system requires that the Calabi-Yau manifold be fibered over the space-time using compensators on ${\cal Y}$. The role of the compensators is to ensure smoothness of the eleven-dimensional metric when the moduli of ${\cal Y}$ depend on the space-time. The Maxwell field Ansatz also implicitly involves the compensators through the frames of the fibration. We examine the equations of motion and discuss the brane distributions on generic internal manifolds that do not have enough symmetry to allow smearing.

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arXiv2017

Asymptotically-flat supergravity solutions deep inside the black-hole regime

We construct an infinite family of smooth asymptotically-flat supergravity solutions that have the same charges and angular momenta as general supersymmetric D1-D5-P black holes, but have no horizon. These solutions resemble the corresponding black hole to arbitrary accuracy outside of the horizon: they have asymptotically flat regions, AdS_3 x S^3 throats and very-near-horizon AdS_2 throats, which however end in a smooth cap rather than an event horizon. The angular momenta of the solutions are general, and in particular can take arbitrarily small values. Upon taking the AdS_3 x S^3 decoupling limit, we identify the holographically-dual CFT states.

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arXiv2017

Supersymmetry and Wrapped Branes in Microstate Geometries

We consider the supergravity back-reaction of M2 branes wrapping around the space-time cycles in 1/8-BPS microstate geometries. We show that such brane wrappings will generically break all the supersymmetries. In particular, all the supersymmetries will be broken if there are such wrapped branes but the net charge of the wrapped branes is zero. We show that if M2 branes wrap a single cycle, or if they wrap a several of co-linear cycles with the same orientation, then the solution will be 1/16-BPS, having two supersymmetries. We comment on how these results relate to using W-branes to understand the microstate structure of 1/8-BPS black holes.

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arXiv2017

Tidal Stresses and Energy Gaps in Microstate Geometries

We compute energy gaps and study infalling massive geodesic probes in the new families of scaling, microstate geometries that have been constructed recently and for which the holographic duals are known. We find that in the deepest geometries, which have the lowest energy gaps, the geodesic deviation shows that the stress reaches the Planck scale long before the probe reaches the cap of the geometry. Such probes must therefore undergo a stringy transition as they fall into microstate geometry. We discuss the scales associated with this transition and comment on the implications for scrambling in microstate geometries.

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arXiv2017

Integrability and Black-Hole Microstate Geometries

We examine some recently-constructed families of asymptotically-AdS$_3 \times$S$^3$ supergravity solutions that have the same charges and mass as supersymmetric D1-D5-P black holes, but that cap off smoothly with no horizon. These solutions, known as superstrata, are quite complicated, however we show that, for an infinite family of solutions, the null geodesic problem is completely integrable, due to the existence of a non-trivial conformal Killing tensor that provides a quadratic conservation law for null geodesics. This implies that the massless scalar wave equation is separable. For another infinite family of solutions, we find that there is a non-trivial conformal Killing tensor only when the left-moving angular momentum of the massless scalar is zero. We also show that, for both these families, the metric degrees of freedom have the form they would take if they arose from a consistent truncation on S$^3$ down to a (2+1)-dimensional space-time. We discuss some of the broader consequences of these special properties for the physics of these black-hole microstate geometries.

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