arXiv subjects

Nicholas P. Warner

Publications and source records attributed to Nicholas P. Warner.

At least 19 recordsLinked to original sources

arXiv2026

Localizing Momentum Waves on Mazes

We examine the proposal and analysis of arXiv:2404.14477 for putting momentum waves on mazes of intersecting M2 and M5 branes by computing a family of simple examples of momentum waves on pure M5 branes. We re-analyze the BPS equations for the near-brane M5-P system with the prescribed supersymmetry structure of the full M2-M5-P system and show that the general linear system obtained in arXiv:2404.14477 captures all of the null momentum waves on the simpler M5-P system. Despite the absence of explicit M2 branes in our examples, we find that the momentum waves still localize on an AdS$_3$ factor of the AdS$_7$ associated with M5 branes, showing that the supersymmetry prescription still reflects the M2-M5-P structure. This momentum localization takes two forms: explicit singular sources and smooth, localized bump functions reflecting ''momentum migration'' that is a feature of other microstate geometries. The simple, physical form of the momentum localization in our examples supports the broader proposal in arXiv:2404.14477 that independent momentum waves can localize at each brane intersection. We suggest further generalizations of momentum waves at brane intersections that could have important implications in holography.

hep-th↗

arXiv2026

Zooming out of AdS$_4 \times$S$^2 \times$S$^2$: The Branes behind the CFT's

We reveal the supersymmetric brane configurations that give rise to AdS$_4\times$S$^2\times$S$^2$ supergravity solutions, which are holographic duals to three-dimensional $N=4$ CFTs or to conformal boundaries and domain walls of four-dimensional $N=4$ SYM. We show that these solutions preserve the same Killing spinors as orthogonal D3, D5 and NS5 branes in flat space, and that the singular sources of these solutions correspond to semi-infinite D3-D5 and D3-NS5 spikes. We track these solutions all the way from the weak-coupling regime of parameters, where the branes do not backreact, to the supergravity regime. We explain how the AdS$_4$ factor arises from certain universal self-similar bending regions of the five-branes, whose steepness is the same as the weak-coupling linking numbers. We also propose a brane configuration that gives rise to the Janus interface solutions. Our construction gives a clear geometric explanation of the Gaiotto-Witten "good-bad-ugly" classification of eight-supercharge theories: only good theories have five-branes that do not cross when back-reacting, and end up sourcing an AdS$_4\times$S$^2\times$S$^2$ solution.

hep-th↗

arXiv2025

Effervescent Spikes in M-theory

AdS$_3 \times$ S$^3 \times$ S$^3$ solutions warped over a Riemann surface, $Σ$, are indexed by a parameter, $γ$, that defines the superconformal algebra, $D(2,1; γ) \oplus D(2,1; γ)$ they preserve. We show that these solutions come from multiple back-reacted M2-M5 spikes, and that different values of $γ$ correspond to different scaling limits of the same M2-M5 solutions. We find that when $γ$ switches from positive to negative, the infrared region of the AdS$_3$ switches from the tip of spikes, far from the M5 branes, to the bottom of the spikes, far from the M2 branes. We also explain how the bubbling negative-$γ$ solutions emerge from the geometric transition of multiple M2-M5 spikes.

hep-th↗

arXiv2025

Effective Microstructure

In AdS$_3$/CFT$_2$ duality, there are large families of smooth, horizonless microstate geometries that correspond to heavy pure states of the dual CFT. The metric and fluxes are complicated functions of up to five coordinates. There are also many duals of heavy pure states that cannot be described in supergravity, but only admit a worldsheet description. Extracting the physical properties of these solutions is technically challenging. In this paper, we show that there are much simpler effective descriptions of these solutions that capture many of their stringy and geometrical features, at the price of sacrificing supergravity smoothness. In particular, the effective description of some families of superstrata, and of certain worldsheet solutions, is given by easy-to-construct three-center solutions. For example, the effective description of a superstratum with a long AdS$_2$ throat is a scaling, three-center solution in which the momentum wave is collapsed to a singular source at one of the three centers. This also highlights how momentum migrates away from the supertube locus in the back-reacted geometry. Our results suggest that effective descriptions can be extended to more general microstates, and that many singular multi-center solutions can in fact correspond to effective descriptions of smooth horizonless microstructure.

hep-th↗

arXiv2025

The Special Locus

The special locus plays an important role in the construction of the non-BPS microstate geometries known as microstrata. These supergravity solutions are dual to combinations of left-moving and right-moving momentum states in the D1-D5 CFT and because supersymmetry is broken the anomalous dimensions of these states are not protected. This means even the simplest combinations of excitations can create a cascade of frequency dependences through the non-linearities of the supergravity interactions. Solutions on the special locus manage to lock some of these anomalous dimensions together and allow one to construct complete solutions using gauged supergravity in three dimensions. In the dual holographic CFT, the special locus has been shown to correspond to creating a "pure" gas of single particle states, however, in supergravity the special locus remains mysterious especially because it does not seem to be defined by a geometric symmetry. In this paper we reveal the supergravity structure of the special locus, first in three-dimensional supergravity and then in the uplift to six dimensions and IIB supergravity. The key insight is that, in three dimensions, a family of dual vector fields must vanish, and this implies that there are algebraic relations between tensor gauge fields in six and ten dimensions. These insights show how one can generalize the special locus Ansatz to more general mode excitations of six-dimensional supergravity. We also construct the full six-dimensional uplift of the simplest special locus.

hep-th↗

arXiv2025

Microstate Geometries

We review the 20-year history of the Microstate Geometry Programme and the essential role that supergravity has played, and will continue to play, in the description of black-hole microstructure.

hep-th↗

arXiv2025

Maze Topiary in Supergravity

We show that the supergravity solutions for 1/4-BPS intersecting systems of M2 and M5 branes are completely characterized by a single ``maze'' function that satisfies a non-linear ``maze'' equation similar to the Monge-Ampère equation. We also show that the near-brane limit of certain intersections are $AdS_3 \times S^3 \times S^3$ solutions warped over a Riemann surface, $Σ$. There is an extensive literature on these subjects and we construct mappings between various approaches and use brane probes to elucidate the relationships between the M2-M5 and AdS systems. We also use dualities to map our results onto other systems of intersecting branes. This work is motivated by the recent realization that adding momentum to M2-M5 intersections gives a supermaze that can reproduce the black-hole entropy without ever developing an event horizon. We take a step in this direction by adding a certain type of momentum charges that blackens the M2-M5 intersecting branes. The near-brane limit of these solutions is a BTZ$^{extremal} \times S^3 \times S^3 \times Σ$ geometry in which the BTZ momentum is a function of the Riemann surface coordinates.

hep-th↗

arXiv2024

The M2-M5 Mohawk

We show that the near-brane back-reaction of M2 branes ending on M5 branes has a rich "spike structure" that is determined by partitioning the numbers of M2 branes that are terminating on groups of M5 branes. The near-brane limit of the metric describing these branes has an AdS$_3$ factor, implying the existence of a dual CFT. Each partition of the M2 and M5 charges among spikes gives rise to a different "mohawk" revealing a new layer of brane fractionation. We conjecture that all these mohawks are dual to ground states of near-brane-intersection CFT's. We show that the supergravity solutions describing these mohawks are part of the large families of AdS$_3$ $\times S^3 \times S^3$ solutions described in [arXiv:1312.5477]. We identify precisely which of these families are relevant to brane intersections and show that the AdS$_3$ invariance emerges from the self-similarity of the spikes.

hep-th↗

arXiv2024

Waves on Mazes

One way to describe the entropy of black holes comes from partitioning momentum charge across fractionated intersecting brane systems. Here we construct $\frac{1}{8}$-BPS solutions by adding momentum to a maze of M2-brane strips stretched between M5 branes. Before the addition of momentum, the $\frac{1}{4}$-BPS supergravity solution describing the maze is governed by a master function obeying a complicated Monge-Ampère equation. Given such a solution, we show that one can add momentum waves without modifying the $\frac{1}{4}$-BPS M2-M5 background. Remarkably, these excitations are fully determined by a layered set of $\textit{linear}$ equations. The fields responsible for carrying the momentum are parameterized by arbitrary functions of a null direction, and have exactly the same structure as in brane world-volume constructions. The fact that the momentum and flux excitations of the M2-M5-P system are governed by a linear structure brings us one step closer to using supergravity solutions to capture the entropy of supersymmetric black-holes.

hep-th↗

arXiv2024

Inscribing geodesic circles on the face of the superstratum

We use families of circular null geodesics as probes of a family of microstate geometries, known as $(1,0,n)$ superstrata. These geometries carry a left-moving momentum wave and the behavior of some of the geodesic probes is very sensitive to this background wave. The left-moving geodesics behave like BPS particles and so can be placed in circular orbits anywhere in the geometry and actually "float" at fixed radius and angle in the three-dimensional "capped BTZ" geometry. The right-moving geodesics behave like non-BPS particles. We show that they provide a simple geometric characterization of the black-hole bound: when the momentum charge of the geometry is below this bound, such geodesics can be placed anywhere, but exceeding the bound, even by a small amount, means these geodesics are restricted to the deep interior of the geometry. We also show that for left-moving string probes, the tidal forces remain comparable with those of global AdS$_3$. Nevertheless, for some of these probes, the "bumps" in the geometry induce an oscillatory mass term and we discuss how this can lead to chaotic scrambling of the state of the string.

hep-th↗

arXiv2023

Microstrata

Microstrata are the non-extremal analogues of superstrata: they are smooth, non-extremal (non-BPS) solitonic solutions to IIB supergravity whose deep-throat limits approximate black holes. Using perturbation theory and numerical methods, we construct families of solutions using a consistent truncation to three-dimensional supergravity. The most general families presented here involve two continuous parameters, or amplitudes, and four quantized parameters that set the angular momenta and energy levels. Our solutions are asymptotic to the vacuum of the D1-D5 system: AdS$_3 \times S^3 \times T^4$. Using holography, we show that the they are dual to multi-particle states in the D1-D5 CFT involving a large number of mutually non-BPS supergravitons and we determine the anomalous dimensions of these states from the binding energies in supergravity. These binding energies are uniformly negative and depend non-linearly on the amplitudes of the states. In one family of solutions, smoothness restricts some of the fields to lie on a special locus of the parameter space. Using precision holography we show that this special locus can be identified with the multi-particle states constructed via the standard OPE of the single-particle constituents. Our numerical analysis shows that microstrata are robust at large amplitudes and the solutions can be obtained to very high precision.

hep-th↗

arXiv2022

Themelia: the irreducible microstructure of black holes

We argue that the fundamental "atomic objects" in string theory are themelia: extended objects that have 16 supersymmetries locally. We show that all existing smooth horizonless microstate geometries can be seen as bound states of themelia, and we conjecture that all such bound states with suitable KKM charges will give rise to microstate geometries. We also construct the most general themelion with a three-torus isometry and show that it interpolates between superstrata and the super-maze.

hep-th↗

arXiv2022

Elliptical and Purely NS Superstrata

We analyze the BPS equations in the ``superstratum sector'' of three-dimensional gauged supergravity. We obtain multi-parameter supersymmetric solutions that include elliptical deformations of the supertubes that underlie standard superstrata. We uplift the three-dimensional solutions to obtain the corresponding six-dimensional geometries. This yields new families of elliptically-deformed, ambi-bolar hyper-Kähler geometries in four dimensions with a non-tri-holomorphic $U(1)$ isometry. We also find a new family of scaling superstrata whose S-dual lives entirely within the NS-sector of supergravity, and will thus be more amenable to exact analysis using string probes. In all these new superstrata, including the scaling ones, if the momentum charge is non-zero we find that the ellipse stays away from the degeneration locus in which the ellipse becomes flat.

hep-th↗

arXiv2022

Fuzzballs and Microstate Geometries: Black-Hole Structure in String Theory

The black-hole information paradox provides one of the sharpest foci for the conflict between quantum mechanics and general relativity and has become the proving-ground of would-be theories of quantum gravity. String theory has made significant progress in resolving this paradox, and has led to the fuzzball and microstate geometry programs. The core principle of these programs is that horizons and singularities only arise if one tries to describe gravity using a theory that has too few degrees of freedom to resolve the physics. String theory has sufficiently many degrees of freedom and this naturally leads to fuzzballs and microstate geometries: The reformation of black holes into objects with neither horizons nor singularities. This not only resolves the paradox but provides new insights into the microstructure of black holes. We summarize the current status of this approach and describe future prospects and additional insights that are now within reach. This paper is an expanded version of our Snowmass White Paper arXiv:2203.04981.

hep-th↗

arXiv2022

Linearizing the BPS Equations with Vector and Tensor Multiplets

We analyse the BPS equations of $\mathcal{N} = (1,0)$ supergravity theory in six dimensions coupled to a vector and tensor multiplet. We show how these BPS equations can be reduced to a set of linear differential equations. This system is triangular in that each layer of equations, while linear, is quadratically sourced by the solutions of the previous layers. We examine several explicit examples and discuss the construction of new families of microstate geometries. We expect that the result presented here will open up new branches of superstrata in which the momentum is encoded in a new class of charge carriers.

hep-th↗

arXiv2022

Snowmass White Paper: Micro- and Macro-Structure of Black Holes

The black-hole information paradox provides a stringent test of would-be theories of quantum gravity. String theory has made significant progress toward a resolution of this paradox, and has led to the fuzzball and microstate geometry programs. The central thesis of these programs is that only string theory has sufficiently many degrees of freedom to resolve black-hole microstructure, and that horizons and singularities are artifacts of attempting to describe gravity using a theory that has too few degrees of freedom to resolve the physics. Fuzzballs and microstate geometries recast black holes within string theory as horizonless and singularity-free objects that not only resolve the paradox but provide new insight into the underlying microstructure. We give an overview of this approach, summarize its current status and describe future prospects and insights that are now within reach.

hep-th↗

arXiv2022

Resolving Black-Hole Microstructure with New Momentum Carriers

All known horizonless black-hole microstate geometries correspond to brane sources that acquire a finite size, and hence break the spherical symmetry of the black hole. We construct, for the first time, solutions with zero horizon area that have the same charges as a three-charge F1-NS5-P Type-IIA black hole and preserve this spherical symmetry. The momentum of these solutions is carried by longitudinal D0-D4 density fluctuations inside the NS5-branes. We argue that these solutions should be interpreted as the long-throat limit of a family of smooth, horizonless microstate geometries, called superstrata, where such geometries degenerate. The existence of these geometries indicates that a finite-size horizon does not appear even in the singular corners of the moduli space of three-charge microstate geometries.

hep-th↗

arXiv2021

New Superstrata from Three-Dimensional Supergravity

We find a two-parameter family of {\it generalized superstrata} that emerge as smooth, supersymmetric solutions in three-dimensional gauged supergravity coupled to additional scalar fields. This new family of generalized superstrata are smooth microstate geometries and may be thought of as supersymmetric Coulomb-branch extensions of the original superstrata in which the underlying supertube undergoes an elliptical deformation. These solutions had already been obtained numerically, and as series solutions, to the equations of motion, and some of them were conjectured to be supersymmetric. Here we prove the supersymmetry of an entire two-parameter family and we obtain a highly non-trivial analytic and smooth solution for a one-parameter limit in which the global symmetry of the metric is enhanced to $SO(3)$. We also confirm that the other known families of microstrata are {\it not} supersymmetric. We conclude with a cursory analysis of some of the singular brane distributions that can be accessed from three-dimensional gauged supergravity while preserving the same supersymmetries as the superstratum, and therefore of the three-charge black hole.

hep-th↗