arXiv subjects

Cynthia Keeler

Publications and source records attributed to Cynthia Keeler.

At least 37 records · Page 2Linked to original sources

arXiv2020

From Navier-Stokes to Maxwell via Einstein

We revisit the cutoff surface formulation of fluid-gravity duality in the context of the classical double copy. The spacetimes in this fluid-gravity duality are algebraically special, with Petrov type II when the spacetime is four dimensional. We find two special classes of fluids whose dual spacetimes exhibit higher algebraic speciality: constant vorticity flows have type D gravity duals, while potential flows map to type N spacetimes. Using the Weyl version of the classical double copy, we construct associated single-copy gauge fields for both cases, finding that constant vorticity fluids map to a solenoid gauge field. Additionally we find the scalar in a potential flow fluid maps to the zeroth copy scalar.

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arXiv2019

Connecting quasinormal modes and heat kernels in 1-loop determinants

We connect two different approaches for calculating functional determinants on quotients of hyperbolic spacetime: the heat kernel method and the quasinormal mode method. For the example of a rotating BTZ background, we show how the image sum in the heat kernel method builds up the logarithms in the quasinormal mode method, while the thermal sum in the quasinormal mode method builds up the integrand of the heat kernel. More formally, we demonstrate how the heat kernel and quasinormal mode methods are linked via the Selberg zeta function. We show that a 1-loop partition function computed using the heat kernel method may be cast as a Selberg zeta function whose zeros encode quasinormal modes. We discuss how our work may be used to predict quasinormal modes on more complicated spacetimes.

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arXiv2019

BTZ one-loop determinants via the Selberg zeta function for general spin

We relate the heat kernel and quasinormal mode methods of computing the 1-loop partition function of arbitrary spin fields on a rotating (Euclidean) BTZ background using the Selberg zeta function associated with $\mathbb{H}^{3}/\mathbb{Z}$, extending (1811.08433). Previously, Perry and Williams showed for a scalar field that the zeros of the Selberg zeta function coincide with the poles of the associated scattering operator upon a relabeling of integers. We extend the integer relabeling to the case of general spin, and discuss its relationship to the removal of non-square-integrable Euclidean zero modes.

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arXiv2019

Towards Bulk Metric Reconstruction from Extremal Area Variations

The Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi formulae suggest that bulk geometry emerges from the entanglement structure of the boundary theory. Using these formulae, we build on a result of Alexakis, Balehowsky, and Nachman to show that in four bulk dimensions, the entanglement entropies of boundary regions of disk topology uniquely fix the bulk metric in any region foliated by the corresponding HRT surfaces. More generally, for a bulk of any dimension $d \geq 4$, knowledge of the (variations of the) areas of two-dimensional boundary-anchored extremal surfaces of disk topology uniquely fixes the bulk metric wherever these surfaces reach. This result is covariant and not reliant on any symmetry assumptions; its applicability thus includes regions of strong dynamical gravity such as the early-time interior of black holes formed from collapse. While we only show uniqueness of the metric, the approach we present provides a clear path towards an explicit spacetime metric reconstruction.

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arXiv2018

Homogeneous Nonrelativistic Geometries as Coset Spaces

We generalize the coset procedure of homogeneous spacetimes in (pseudo-)Riemannian geometry to non-Lorentzian geometries. These are manifolds endowed with nowhere vanishing invertible vielbeins that transform under local non-Lorentzian tangent space transformations. In particular, we focus on nonrelativistic symmetry algebras that give rise to (torsional) Newton-Cartan geometries, for which we demonstrate how the Newton-Cartan metric complex is determined by degenerate co- and contravariant symmetric bilinear forms on the coset. In specific cases, we also show the connection of the resulting nonrelativistic coset spacetimes to pseudo-Riemannian cosets via Inönü-Wigner contraction of relativistic algebras as well as null reduction. Our construction is of use for example when considering limits of the AdS/CFT correspondence in which nonrelativistic spacetimes appear as gravitational backgrounds for nonrelativistic string or gravity theories.

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arXiv2017

Tweaking one-loop determinants in AdS$_3$

We revisit the subject of one-loop determinants in AdS$_3$ gravity via the quasinormal mode method. Our goal is to evaluate a one-loop determinant with chiral boundary conditions for the metric field; chirality is achieved by imposing Dirichlet boundary conditions on certain components while others satisfy Neumann. Along the way, we give a generalization of the quasinormal mode method for stationary (non-static) thermal backgrounds, and propose a treatment for Neumann boundary conditions in this framework. We evaluate the graviton one-loop determinant on the Euclidean BTZ background with parity-violating boundary conditions (CSS), and find excellent agreement with the dual warped CFT. We also discuss a more general falloff in AdS$_3$ that is related to two dimensional quantum gravity in lightcone gauge. The behavior of the ghost fields under both sets of boundary conditions is novel and we discuss potential interpretations.

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arXiv2016

Boundary Causality vs Hyperbolicity for Spherical Black Holes in Gauss-Bonnet

We explore the constraints boundary causality places on the allowable Gauss-Bonnet gravitational couplings in asymptotically AdS spaces, specifically considering spherical black hole solutions. We additionally consider the hyperbolicity properties of these solutions, positing that hyperbolicity-violating solutions are sick solutions whose causality properties provide no information about the theory they reside in. For both signs of the Gauss-Bonnet coupling, spherical black holes violate boundary causality at smaller absolute values of the coupling than planar black holes do. For negative coupling, as we tune the Gauss-Bonnet coupling away from zero, both spherical and planar black holes violate hyperbolicity before they violate boundary causality. For positive coupling, the only hyperbolicity-respecting spherical black holes which violate boundary causality do not do so appreciably far from the planar bound. Consequently, eliminating hyperbolicity-violating solutions means the bound on Gauss-Bonnet couplings from the boundary causality of spherical black holes is no tighter than that from planar black holes.

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arXiv2016

Partition Functions with spin in AdS_2 via Quasinormal Mode Methods

We extend the results of arXiv:1401.7016, computing one loop partition functions for massive fields with spin half in AdS_2 using the quasinormal mode method proposed by Denef, Hartnoll, and Sachdev in arXiv:0908.2657. We find the finite representations of SO(2,1) for spin zero and spin half, consisting of a highest weight state |h\rangle and descendants with non-unitary values of h. These finite representations capture the poles and zeroes of the one loop determinants. Together with the asymptotic behavior of the partition functions (which can be easily computed using a large mass heat kernel expansion), these are sufficient to determine the full answer for the one loop determinants. We also discuss extensions to higher dimensional AdS_{2n} and higher spins.

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arXiv2016

Universal features of Lifshitz Green's functions from holography

We examine the behavior of the retarded Green's function in theories with Lifshitz scaling symmetry, both through dual gravitational models and a direct field theory approach. In contrast with the case of a relativistic CFT, where the Green's function is fixed (up to normalization) by symmetry, the generic Lifshitz Green's function can a priori depend on an arbitrary function $\mathcal G(\hatω)$, where $\hatω=ω/|\vec k|^z$ is the scale-invariant ratio of frequency to wavenumber, with dynamical exponent $z$. Nevertheless, we demonstrate that the imaginary part of the retarded Green's function (i.e. the spectral function) of scalar operators is exponentially suppressed in a window of frequencies near zero. This behavior is universal in all Lifshitz theories without additional constraining symmetries. On the gravity side, this result is robust against higher derivative corrections, while on the field theory side we present two $z=2$ examples where the exponential suppression arises from summing the perturbative expansion to infinite order.

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arXiv2016

On the reconstruction of Lifshitz spacetimes

We consider the reconstruction of a Lifshitz spacetime from three perspectives: differential entropy (or "hole-ography"), causal wedges and entanglement wedges. We find that not all time-varying bulk curves in vacuum Lifshitz can be reconstructed via the differential entropy approach, adding a caveat to the general analysis of \cite{Headrick:2014eia}. We show that the causal wedge for Lifshitz spacetimes degenerates, while the entanglement wedge requires the additional consideration of a set of boundary-emanating light-sheets. The need to include bulk surfaces with no clear field theory interpretation in the differential entropy construction and the change in the entanglement wedge formation both serve as warnings against a naive application of holographic entanglement entropy proposals in Lifshitz spacetimes.

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arXiv2015

Schrödinger Holography with $z=2$

We investigate holography for asymptotically Schrödinger spacetimes, using a frame formalism based on the anisotropic scaling symmetry. We build on our previous work on $z<2$ to propose a dictionary for $z=2$. For $z=2$, the scaling symmetry does not act on the additional null direction, which implies that in our dictionary it does not correspond to one of the field theory directions. This is significantly different from previous analyses based on viewing Schrödinger as a deformation of AdS. We study this dictionary in the linearised theory and in an asymptotic expansion. We show that a solution exists in an asymptotic expansion for arbitrary sources for the relevant operators in the stress energy complex.

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arXiv2014

Schrodinger Holography for z<2

We investigate holography for asymptotically Schrodinger spacetimes, using a frame formalism. Our dictionary is based on the anisotropic scaling symmetry. We consider z <2, where the holographic dictionary is cleaner; we make some comments on z=2. We propose a definition of asymptotically locally Schrodinger spacetime where the leading components of the frame fields provide suitable geometric boundary data. We show that an asymptotic expansion exists for generic boundary data satisfying our boundary conditions for z<2.

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arXiv2014

Grassmannians for scattering amplitudes in 4d $\mathcal{N}=4$ SYM and 3d ABJM

Scattering amplitudes in 4d $\mathcal{N}=4$ super Yang-Mills theory (SYM) can be described by Grassmannian contour integrals whose form depends on whether the external data is encoded in momentum space, twistor space, or momentum twistor space. After a pedagogical review, we present a new, streamlined proof of the equivalence of the three integral formulations. A similar strategy allows us to derive a new Grassmannian integral for 3d $\mathcal{N}=6$ ABJM theory amplitudes in momentum twistor space: it is a contour integral in an orthogonal Grassmannian with the novel property that the internal metric depends on the external data. The result can be viewed as a central step towards developing an amplituhedron formulation for ABJM amplitudes. Various properties of Grassmannian integrals are examined, including boundary properties, pole structure, and a homological interpretation of the global residue theorems for $\mathcal{N}=4$ SYM.

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arXiv2014

Hidden horizons in non-relativistic AdS/CFT

We study boundary Green's functions for spacetimes with non-relativistic scaling symmetry. For this class of backgrounds, scalar modes with large transverse momentum, or equivalently low frequency, have an exponentially suppressed imprint on the boundary. We investigate the effect of these modes on holographic two-point functions. We find that the boundary Green's function is generically insensitive to horizon features on small transverse length scales. We explicitly demonstrate this insensitivity for Lifshitz z=2, and then use the WKB approximation to generalize our findings to Lifshitz z>1 and RG flows with a Lifshitz-like region. We also comment on the analogous situation in Schroedinger spacetimes. Finally, we exhibit the analytic properties of the Green's function in these spacetimes.

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arXiv2014

Partition Functions in Even Dimensional AdS via Quasinormal Mode Methods

In this note, we calculate the one-loop determinant for a massive scalar (with conformal dimension $Δ$) in even-dimensional AdS$_{d+1}$ space, using the quasinormal mode method developed in arXiv:0908.2657 by Denef, Hartnoll, and Sachdev. Working first in two dimensions on the related Euclidean hyperbolic plane $H_2$, we find a series of zero modes for negative real values of $Δ$ whose presence indicates a series of poles in the one-loop partition function $Z(Δ)$ in the $Δ$ complex plane; these poles contribute temperature-independent terms to the thermal AdS partition function computed in arXiv:0908.2657. Our results match those in a series of papers by Camporesi and Higuchi, as well as Gopakumar et al. in arXiv:1103.3627 and Banerjee et al. in arXiv:1005.3044. We additionally examine the meaning of these zero modes, finding that they Wick-rotate to quasinormal modes of the AdS$_2$ black hole. They are also interpretable as matrix elements of the discrete series representations of $SO(2,1)$ in the space of smooth functions on $S^1$. We generalize our results to general even dimensional AdS$_{2n}$, again finding a series of zero modes which are related to discrete series representations of $SO(2n,1)$, the motion group of $H_{2n}$.

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arXiv2014

Logarithmic Corrections to $N \geq 2$ Black Hole Entropy

We revisit the computation of logarithmic corrections to black holes with N equal or greater than 2 supersymmetry. We employ an on-shell method that takes advantage of the symmetries in the AdS(2) x S**2 near horizon geometry. For bulk modes interactions are incorporated through the spectrum of chiral primaries that we derive afresh. The spectrum of boundary states is computed explicitly by analyzing gauge variations. Elementary heat kernels in 4D and 2D then give the logarithmic corrections to the black hole entropy. Our computation represents a streamlined and simplified derivation that agrees with the results recently found by A. Sen.

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arXiv2013

What do non-relativistic CFTs tell us about Lifshitz spacetimes?

We study the reconstructability of (d+2)-dimensional bulk spacetime from (d+1)-dimensional boundary data, particularly concentrating on backgrounds which break (d+1)-dimensional Lorentz invariance. For a large class of such spacetimes, there exist null geodesics which do not reach the boundary. Therefore classically we expect some information is trapped in the bulk and thus invisible at the boundary. We show that this classical intuition correctly predicts the quantum situation: whenever there are null geodesics which do not reach the boundary, there are also "trapped scalar modes" whose boundary imprint is exponentially suppressed. We use these modes to show that no smearing function exists for pure Lifshitz spacetime, nor for any flow which includes a Lifshitz region. Indeed, for any (planar) spacetime which breaks (d+1)-dimensional Lorentz invariance at any radius, we show that local boundary data cannot reconstruct complete local bulk data.

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arXiv2013

Scalar Boundary Conditions in Lifshitz Spacetimes

We investigate the conditions imposable on a scalar field at the boundary of the so- called Lifshitz spacetime which has been proposed as the dual to Lifshitz field theories. For effective mass squared between -(d+z-1)^2/4 and z^2-(d+z-1)^2/4, we find a one-parameter choice of boundary condition type. The bottom end of this range corresponds to a Breitenlohner-Freedman bound; below it, the Klein-Gordon operator need not be positive, so we cannot make sense of the dynamics. Above the top end of the range, only one boundary condition type is available; here we expect compact initial data will remain compact in the future.

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