arXiv subjects

Nicholas P. Warner

Publications and source records attributed to Nicholas P. Warner.

At least 55 records · Page 3Linked to original sources

arXiv2017

M-theory Superstrata and the MSW String

The low-energy description of wrapped M5 branes in compactifications of M-theory on a Calabi-Yau threefold times a circle is given by a conformal field theory studied by Maldacena, Strominger and Witten and known as the MSW CFT. Taking the threefold to be T$^6$ or K3xT$^2$, we construct a map between a sub-sector of this CFT and a sub-sector of the D1-D5 CFT. We demonstrate this map by considering a set of D1-D5 CFT states that have smooth horizonless bulk duals, and explicitly constructing the supergravity solutions dual to the corresponding states of the MSW CFT. We thus obtain the largest known class of solutions dual to MSW CFT microstates, and demonstrate that five-dimensional ungauged supergravity admits much larger families of smooth horizonless solutions than previously known.

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arXiv2016

Boundary Terms and Three-Point Functions: An AdS/CFT Puzzle Resolved

${\cal N} = 8$ superconformal field theories, such as the ABJM theory at Chern-Simons level $k=1$ or $2$, contain 35 scalar operators ${\cal O}_{IJ}$ with $Δ=1$ in the ${\bf 35}_v$ representation of SO(8). The 3-point correlation function of these operators is non-vanishing, and indeed can be calculated non-perturbatively in the field theory. But its AdS$_4$ gravity dual, obtained from gauged ${\cal N}=8$ supergravity, has no cubic $A^3$ couplings in its Lagrangian, where $A^{IJ}$ is the bulk dual of ${\cal O}_{IJ}$. So conventional Witten diagrams cannot furnish the field theory result. We show that the extension of bulk supersymmetry to the AdS$_4$ boundary requires the introduction of a finite $A^3$ counterterm that does provide a perfect match to the 3-point correlator. Boundary supersymmetry also requires infinite counterterms which agree with the method of holographic renormalization. The generating functional of correlation functions of the $Δ=1$ operators is the Legendre transform of the on-shell action, and the supersymmetry properties of this functional play a significant role in our treatment.

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arXiv2016

Smooth horizonless geometries deep inside the black-hole regime

We construct the first family of horizonless supergravity solutions that have the same mass, charges and angular momenta as general supersymmetric rotating D1-D5-P black holes in five dimensions. This family includes solutions with arbitrarily small angular momenta, deep within the regime of quantum numbers and couplings for which a large classical black hole exists. These geometries are well-approximated by the black-hole solution, and in particular exhibit the same near-horizon throat. Deep in this throat, the black-hole singularity is resolved into a smooth cap. We also identify the holographically-dual states in the N=(4,4) D1-D5 orbifold CFT. Our solutions are among the states counted by the CFT elliptic genus, and provide examples of smooth microstate geometries within the ensemble of supersymmetric black-hole microstates.

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arXiv2016

Momentum Fractionation on Superstrata

Superstrata are bound states in string theory that carry D1, D5, and momentum charges, and whose supergravity descriptions are parameterized by arbitrary functions of (at least) two variables. In the D1-D5 CFT, typical three-charge states reside in high-degree twisted sectors, and their momentum charge is carried by modes that individually have fractional momentum. Understanding this momentum fractionation holographically is crucial for understanding typical black-hole microstates in this system. We use solution-generating techniques to add momentum to a multi-wound supertube and thereby construct the first examples of asymptotically-flat superstrata. The resulting supergravity solutions are horizonless and smooth up to well-understood orbifold singularities. Upon taking the AdS3 decoupling limit, our solutions are dual to CFT states with momentum fractionation. We give a precise proposal for these dual CFT states. Our construction establishes the very nontrivial fact that large classes of CFT states with momentum fractionation can be realized in the bulk as smooth horizonless supergravity solutions.

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arXiv2015

$\mathcal{N}=2$ Supersymmetric Janus Solutions and Flows: From Gauged Supergravity to M Theory

We investigate a family of SU(3)$\times$U(1)$\times$U(1)-invariant holographic flows and Janus solutions obtained from gauged $\mathcal{N}=8$ supergravity in four dimensions. We give complete details of how to use the uplift formulae to obtain the corresponding solutions in M theory. While the flow solutions appear to be singular from the four-dimensional perspective, we find that the eleven-dimensional solutions are much better behaved and give rise to interesting new classes of compactification geometries that are smooth, up to orbifolds, in the infra-red limit. Our solutions involve new phases in which M2 branes polarize partially or even completely into M5 branes. We derive the eleven-dimensional supersymmetries and show that the eleven-dimensional equations of motion and BPS equations are indeed satisfied as a consequence of their four-dimensional counterparts. Apart from elucidating a whole new class of eleven-dimensional Janus and flow solutions, our work provides extensive and highly non-trivial tests of the recently-derived uplift formulae.

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arXiv2015

Flowing to Higher Dimensions: A New Strongly-Coupled Phase on M2 Branes

We describe a one-parameter family of new holographic RG flows that start from $AdS_4 \times S^7$ and go to $\widehat{AdS_5} \times {\cal B}_6$, where ${\cal B}_6$ is conformal to a Kähler manifold and $\widehat{AdS_5}$ is Poincaré $AdS_5$ with one spatial direction compactified and fibered over ${\cal B}_6$. The new solutions "flow up dimensions," going from the $(2+1)$-dimensional conformal field theory on M2 branes in the UV to a $(3+1)$-dimensional field theory on intersecting M5 branes in the infra-red. The M2 branes completely polarize into M5 branes along the flow and the Poincaré sections of the $\widehat{AdS_5}$ are the $(3+1)$-dimensional common intersection of the M5 branes. The emergence of the extra dimension in the infra-red suggests a new strongly-coupled phase of the M2 brane and ABJM theories in which charged solitons are becoming massless. The flow solution is first analyzed by finding a four-dimensional $N \! = \! 2$ supersymmetric flow in $N \! = \! 8$ gauged supergravity. This is then generalized to a one parameter family of non-supersymmetric flows. The infra-red limit of the solutions appears to be quite singular in four dimensions but the uplift to eleven-dimensional supergravity is remarkable and regular (up to orbifolding). Our construction is a non-trivial application of the recently derived uplift formulae for fluxes, going well beyond the earlier constructions of stationary points solutions. The eleven-dimensional supersymmetry is also analyzed and shows how, for the supersymmetric flow, the M2-brane supersymmetry in the UV is polarized entirely into M5-brane supersymmetry in the infra-red.

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arXiv2015

Habemus Superstratum! A constructive proof of the existence of superstrata

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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arXiv2014

On the Oscillation of Species

We describe a new class of BPS objects called magnetubes: their supersymmetry is determined by their magnetic charges, while their electric charges can oscillate freely between different species. We show how to incorporate these objects into microstate geometries and create BPS solutions in which the charge densities rotate through different U(1) species as one moves around a circle within the microstate geometry. Our solutions have the same "time-like" supersymmetry as five-dimensional, three-charge black holes but, in various parts of the solution, the supersymmetry takes the "null" form that is normally associated with magnetic charges. It is this property that enables the species oscillation of magnetubes to be compatible with supersymmetry. We give an example in which the species oscillate non-trivially around a circle within a microstate geometry, and yet the energy-momentum tensor and metric are completely independent of this circle: only the amplitude of the oscillation influences the metric.

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arXiv2014

Black-Hole Entropy from Supergravity Superstrata States

There are, by now, several arguments that superstrata, which represent D1-D5-P bound states that depend upon arbitrary functions of two variables and that preserve four supersymmetries, exist in string theory, and that their gravitational back-reaction results in smooth horizonless solutions. In this paper we examine the shape and density modes of the superstratum and give strong evidence that the back-reacted supergravity solution allows for fluctuation modes whose quantization reproduces the entropy growth of black holes as a function of the charges. In particular, we argue that the shape modes of the superstratum that lie purely within the non-compact space-time directions account for at least $1/\sqrt{6}$ of the entropy of the D1-D5-P black hole and propose a way in which the rest of the entropy could be captured by superstratum fluctuations. We complete the picture by conjecturing a relationship between bound states of multiple superstrata and momentum excitations of different twisted sectors of the dual CFT.

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arXiv2014

Coiffured Black Rings

We describe a new type of hair on supersymmetric black string and black ring solutions, which produces the largest known violation of black hole uniqueness, parameterized by an arbitrary function and hence an infinite number of continuous parameters. The new solutions can have non-trivial density profiles for the electric fields along the horizon, and yet have a geometry that is regular, although generically not infinitely differentiable, at the horizon. Both neutral and charged probes can cross the horizon without experiencing divergent forces. We also find restricted examples, parameterized by a few arbitrary continuous parameters, where the charge densities fluctuate but the metric does not and hence is completely differentiable. Our new class of solutions owes its existence to a mechanism reminiscent of the Q-ball: in the simplest examples the metric has more symmetry than the matter that supports it.

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arXiv2013

Supersymmetric Janus Solutions in Four Dimensions

We use maximal gauged supergravity in four dimensions to construct the gravity dual of a class of supersymmetric conformal interfaces in the theory on the world-volume of multiple M2-branes. We study three classes of examples in which the $(1+1)$-dimensional defects preserve $(4,4)$, $(0,2)$ or $(0,1)$ supersymmetry. Many of the solutions have the maximally supersymmetric $AdS_4$ vacuum dual to the $\mathcal{N}=8$ ABJM theory on both sides of the interface. We also find new special classes of solutions including one that interpolates between the maximally supersymmetric vacuum and a conformal fixed point with $\mathcal{N}=1$ supersymmetry and $G_2$ global symmetry. We find another solution that interpolates between two distinct conformal fixed points with $\mathcal{N}=1$ supersymmetry and $G_2$ global symmetry. In eleven dimensions, this $G_2$ to $G_2$ solution corresponds to a domain wall across which a magnetic flux reverses orientation.

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arXiv2013

Resolving the Structure of Black Holes: Philosophizing with a Hammer

We give a broad conceptual review of what we have learned about black holes and their microstate structure from the study of microstate geometries and their string theory limits. We draw upon general relativity, supergravity, string theory and holographic field theory to extract universal ideas and structural features that we expect to be important in resolving the information problem and understanding the microstate structure of Schwarzschild and Kerr black holes. In particular, we emphasize two conceptually and physically distinct ideas, with different underlying energy scales: a) the transition that supports the microstate structure and prevents the formation of a horizon and b) the representation of the detailed microstate structure itself in terms of fluctuations around the transitioned state. We also show that the supergravity mechanism that supports microstate geometries becomes, in the string theory limit, either brane polarization or the excitation of non-Abelian degrees of freedom. We thus argue that if any mechanism for supporting structure at the horizon scale is to be given substance within string theory then it must be some manifestation of microstate geometries.

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arXiv2013

Doubly-Fluctuating BPS Solutions in Six Dimensions

We analyze the BPS solutions of minimal supergravity coupled to an anti-self-dual tensor multiplet in six dimensions and find solutions that fluctuate non-trivially as a function of two variables. We consider families of solutions coming from KKM monopoles fibered over Gibbons-Hawking metrics or, equivalently, non-trivial T^2 fibrations over an R3 base. We find smooth microstate geometries that depend upon many functions of one variable, but each such function depends upon a different direction inside the T^2 so that the complete solution depends non-trivially upon the whole T^2 . We comment on the implications of our results for the construction of a general superstratum.

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arXiv2013

Almost BPS but still not renormalized

A key feature of BPS multi-center solutions is that the equations controlling the positions of these centers are not renormalized as one goes from weak to strong coupling. In particular, this means that brane probes can capture the same information as the fully back-reacted supergravity solution. We investigate this non-renormalization property for non-supersymmetric, extremal "almost-BPS" solutions at intermediate coupling when one of the centers is considered as a probe in the background created by the other centers. We find that despite the lack of supersymmetry, the probe action reproduces exactly the equations underlying the fully back-reacted solution, which indicates that these equations also do not receive quantum corrections. In the course of our investigation we uncover the relation between the charge parameters of almost-BPS supergravity solutions and their quantized charges, which solves an old puzzle about the quantization of the charges of almost-BPS solutions.

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arXiv2013

Multi-Superthreads and Supersheets

We obtain new BPS solutions of six-dimensional, N = 1 supergravity coupled to a tensor multiplet. These solutions are sourced by multiple "superthreads" carrying D1-D5-P charges and two magnetic dipole charges. These new solutions are sourced by multiple threads with independent and arbitrary shapes and include new shape-shape interaction terms. Because the individual superthreads can be given independent profiles, the new solutions can be smeared together into continuous "supersheets," described by arbitrary functions of two variables. The supersheet solutions have singularities like those of the three-charge, two dipole-charge generalized supertube in five dimensions and we show how such five-dimensional solutions emerge from a very simple choice of profiles. The new solutions obtained here also represent an important step in finding superstrata, which are expected to play a role in the description of black-hole microstates, due to their ability to store a large amount of entropy in their two-dimensional profile.

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arXiv2012

On Supersymmetric Flux Solutions of M-theory

Motivated by the geometric structures of supersymmetric holographic RG-flows, we scan for N=2 AdS_4 solutions in M-theory. One particularly well understood holographic RG flow in M-theory is dual to a mass deformation of the N=8 Chern-Simons theory. We utilize an Ansatz which is a natural generalization of this background in our scan. We find a single new solution with non-trivial internal flux and the topology of S^7. Interestingly, despite our Ansatz being quite general, within our system we rule out solutions with internal flux on more general Sasaki-Einstein seven manifolds.

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arXiv2012

New Supersymmetric Bubbles on AdS_3xS^3

We find a large new class of explicit solutions preserving four supercharges in six-dimensional supergravity. The solutions are determined by solving a linear system of equations on a four-dimensional Kahler base studied by LeBrun. For particular choices of the parameters, we find regular backgrounds that are asymptotic to the near-horizon limit of the D1-D5-P black string. Holography implies that these backgrounds should be dual to 1/4-BPS states in the D1-D5-P CFT.

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arXiv2012

Supersymmetric Solutions in Six Dimensions: A Linear Structure

The equations underlying all supersymmetric solutions of six-dimensional minimal ungauged supergravity coupled to an anti-self-dual tensor multiplet have been known for quite a while, and their complicated non-linear form has hindered all attempts to systematically understand and construct BPS solutions. In this paper we show that, by suitably re-parameterizing these equations, one can find a structure that allows one to construct supersymmetric solutions by solving a sequence of linear equations. We then illustrate this method by constructing a new class of geometries describing several parallel spirals carrying D1, D5 and P charge and parameterized by four arbitrary functions of one variable. A similar linear structure is known to exist in five dimensions, where it underlies the black hole, black ring and corresponding microstate geometries. The unexpected generalization of this to six dimensions will have important applications to the construction of new, more general such geometries.

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