arXiv subjects

Christopher Eling

Publications and source records attributed to Christopher Eling.

At least 19 recordsLinked to original sources

arXiv2025

Topology and the Conformal Invariance of Nodal Lines in Two-Dimensional Active Scalar Turbulence

The inverse cascade in two-dimensional hydrodynamic turbulence exhibits a mysterious phenomenon. Numerical simulations have shown that the nodal isolines of certain scalars actively transported in the flow (eg, the vorticity in Navier-Stokes theory) obey Schramm-Loewner evolution (SLE), which indicates the presence of conformal invariance. Therefore, these turbulent isolines are somehow in the same class as cluster boundaries in equilibrium statistical mechanical models at criticality, such as critical percolation. In this paper, we propose that the inverse cascade is characterized by a local energy (or in some cases, enstrophy) flux field that spontaneously breaks time reversal invariance. The turbulent state consists of random constant flux domains, with the nodal isolines acting as domain walls where the local flux vanishes. The generalized circulation of the domains is proportional to a topological winding number. We argue that these turbulent states are gapped states, in analogy with quantum Hall systems. The turbulent flow consists of many strongly coupled vortices that are analogous to quasi-particles. The nodal isolines are associated with the gapless topological degrees of freedom in the flow, where scale invariance is enhanced to conformal invariance. We introduce a concrete model of this behavior using a two-dimensional effective theory involving the canonical Clebsch scalars. This theory has patch solutions that exhibit power law scaling. The fractional winding number associated with the patches can be related to the Kolmogorov-Kraichnan scaling dimension of the corresponding fluid theory. We argue that the fully developed inverse cascade is a scale invariant gas of these patches. This theory has a conformally invariant sector described by a Liouville conformal field theory whose central charge is fixed by the fractional winding number.

hep-th↗

arXiv2023

A gauge theory for the 3+1 dimensional incompressible Euler equations

We show that the incompressible Euler equations in three spatial dimensions can be expressed in terms of an abelian gauge theory with a topological BF term. A crucial part of the theory is a 3-form field strength, which is dual to a material invariant local helicity in the fluid. In one version of the theory, there is an additional 2-form field strength, with the magnetic field corresponding to fluid vorticity and the electric field identified with the cross-product of the velocity and the vorticity. In the second version, the 2-form field strength is instead expressed in terms of Clebsch scalars. We discuss the theory in the presence of the boundary and argue that edge modes may be present in the dual description of fluid flows with a boundary.

hep-th↗

arXiv2023

A gauge theory for the 2+1 dimensional incompressible Euler equations

We show that in two dimensions the incompressible Euler equations can be re-expressed in terms of an abelian gauge theory with a Chern-Simons term. The magnetic field corresponds to fluid vorticity and the electric field is the product of the vorticity and the gradient of the stream function. This picture can be extended to active scalar models, including the surface quasi-geostrophic equation. We examine the theory in the presence of a boundary and show that the Noether charge algebra is a Kac-Moody algebra. We argue that this symmetry is associated with the nodal lines of zero magnetic field.

hep-th↗

arXiv2017

Holography and $AdS_2$ gravity with a dynamical aether

We study two-dimensional Einstein-aether (or equivalently Ho\v{r}ava-Lifshitz) gravity, which has an $AdS_2$ solution. We examine various properties of this solution in the context of holography. We first show that the asymptotic symmetry group is the full set of time reparametrizations, the one-dimensional conformal group. At the same time there are configurations with finite energy and temperature, which indicate a violation of the Ward identity associated with one-dimensional conformal invariance. These solutions are characterized by a universal causal horizon and we show that the associated entropy of the universal horizon scales with the logarithm of the temperature. We discuss the puzzles associated with this result and argue that the violation of the Ward identity is associated with a type of explicit breaking of time reparametrizations in the hypothetical $0+1$ dimensional dual system.

hep-th↗

arXiv2016

Spontaneously Broken Asymptotic Symmetries and an Effective Action for Horizon Dynamics

Asymptotic spacetime symmetries have been conjectured to play an important role in quantum gravity. In this paper we study the breaking of asymptotic symmetries associated with a null horizon boundary. In two-dimensions, these symmetries are reparametrizations of the time parameter on the horizon. We show how this horizon reparametrization symmetry is explicitly and spontaneously broken in dilaton gravity and construct an effective action for these pseudo-Goldstone modes using the on-shell gravitational action for a null boundary. The variation of this action yields the horizon constraint equation. This action is invariant under a 2 parameter subgroup of $SL(2)$ transformations, whose Noether charges we interpret via the membrane paradigm. We place these results in the context of recent work on the near $AdS_2$/ near $CFT_1$ correspondence. In this setting the horizon action characterizes the infrared regime near the horizon and has a hydrodynamical sigma model form. We also discuss our construction in General Relativity. In the three-dimensional case there is a natural generalization of our results. However, in higher dimensions, the variation of the effective action only yields the Raychaudhuri equation for small perturbations of the horizon.

hep-th↗

arXiv2016

New Asymptotically Lifshitz Black Holes in Horava gravity

We study asymptotically Lifshitz solutions with critical exponent $z \neq 1$ in Horava gravity in three and four spacetime dimensions. For $z=2$ and $z=3/2$, we find a novel class of numerical solutions with regular universal horizon, but are characterized by non-analytic behavior near infinity. In the interior, inside the universal horizon, the unit timelike vector field associated with the preferred time foliation exhibits oscillatory behavior, qualitatively similar to that found earlier in asymptotically flat solutions. For $z>2$ no solutions of this type appear to exist. We comment on potential applications to holographic Lifshitz dualities.

hep-th↗

arXiv2016

On the Membrane Paradigm and Spontaneous Breaking of Horizon BMS Symmetries

We consider a BMS-type symmetry action on isolated horizons in asymptotically flat spacetimes. From the viewpoint of the non-relativistic field theory on a horizon membrane, supertranslations shift the field theory spatial momentum. The latter is related by a Ward identity to the particle number symmetry current and is spontaneously broken. The corresponding Goldstone boson shifts the horizon angular momentum and can be detected quantum mechanically. Similarly, area preserving superrotations are spontaneously broken on the horizon membrane and we identify the corresponding gapless modes. In asymptotically AdS spacetimes we study the BMS-type symmetry action on the horizon in a holographic superfluid dual. We identify the horizon supertranslation Goldstone boson as the holographic superfluid Goldstone mode.

hep-th↗

arXiv2015

The Anomalous Scaling Exponents of Turbulence in General Dimension from Random Geometry

We propose an exact analytical formula for the anomalous scaling exponents of inertial range structure functions in incompressible fluid turbulence. The formula is a gravitational Knizhnik-Polyakov-Zamolodchikov (KPZ)-type relation, and is valid in any number of space dimensions. It incorporates intermittency by gravitationally dressing the Kolmogorov linear scaling via a coupling to a random geometry. The formula has one real parameter $γ$ that depends on the number of space dimensions. The scaling exponents satisfy the convexity inequality, and the supersonic bound constraint. They agree with the experimental and numerical data in two and three space dimensions, and with numerical data in four space dimensions. Intermittency increases with $γ$, and in the infinite $γ$ limit the scaling exponents approach the value one, as in Burgers turbulence. At large $n$ the $n$th order exponent scales as $\sqrt{n}$. We discuss the relation between fluid flows and black hole geometry that inspired our proposal.

nlin.CD↗

arXiv2014

Horava-Lifshitz Black Hole Hydrodynamics

We consider the holographic hydrodynamics of black holes in generally covariant gravity theories with a preferred time foliation. Gravitational perturbations in these theories have spin two and spin zero helicity modes with generically different speeds. The black hole solutions possess a spacelike causal boundary called the universal horizon. We relate the flux of the spin zero perturbation across the universal horizon to the new dissipative transport in Lifshitz field theory hydrodynamics found in arXiv:1304.7481. We construct in detail the hydrodynamics of one such black hole solution, and calculate the ratio of the shear viscosity to the entropy density.

hep-th↗

arXiv2013

Holographic Vorticity in the Fluid/Gravity Correspondence

The vorticity statistics characterises both the direct and the inverse turbulent cascades of two-dimensional fluid flows. The fluid/gravity correspondence relates fluid flows to black brane dynamics. We construct the holographic vorticity for relativistic and non-relativistic fluids in terms of the gravitational black brane data, and relate it to the horizon vorticity expressed as a Weyl scalar. We discuss the statistical scaling structure of the horizon geometry.

hep-th↗

arXiv2013

Entanglement and Thermal Entropy of Gauge Fields

We consider the universal logarithmic divergent term in the entanglement entropy of gauge fields in the Minkowski vacuum with an entangling sphere. Employing the mapping in arXiv:1102.0440, we analyze the corresponding thermal entropy on open Einstein universe and on the static patch of de Sitter. Using the heat kernel of the vector Laplacian we resolve a discrepancy between the free field calculation and the expected Euler conformal anomaly. The resolution suggests a modification of the well known formulas for the vacuum expectation value of the spin-1 energy-momentum tensor on conformally flat space-times.

hep-th↗

arXiv2013

Challenging the generalized second law

The generalized second law (GSL) of black hole thermodynamics states that the sum of changes in black hole entropy and the ordinary entropy of matter and fields outside the hole must be non-negative. In the classical limit, the GSL reduces to Hawking's area theorem. Neither law identifies the specific effects which makes it work in particular situations. Motivated by Davies' recent gedanken experiment he used to infer a bound on the size of the fine structure constant from the GSL, we study a series of variants in which an electric test charge is lowered to a finite radius and then dropped into a Schwarzschild, a near-extremal magnetic Reissner-Nordstrom or a near-extremal Kerr black hole. For a classical charge, we demonstrate that a specific "backreaction" effect is responsible for protecting the area theorem in the near-extremal examples. For the magnetically charged Reissner-Nordstrom hole an area theorem violation is defused by taking into account a subtle source of repulsion of the charge: the spinning up of the black hole in the process of bringing the charge down to its dropping point. In Kerr hole case, the electric self-force on the charge is sufficient to right matters. However, in all experiments involving an elementary charge, the full GSL would apparently be violated were the fine structure constant greater than about order unity. We argue that in this case a quantum effect, the Unruh-Wald quantum buoyancy, may protect the GSL.

gr-qc↗

arXiv2013

Conformal Anomalies in Hydrodynamics

We study the effect of conformal anomalies on the hydrodynamic description of conformal field theories in even spacetime dimensions. We consider equilibrium curved backgrounds characterized by a time-like Killing vector and construct a local low energy effective action that captures the conformal anomalies. Using as a special background the Rindler spacetime we derive a formula for the anomaly effect on the hydrodynamic pressure. We find that this anomalous effect is only due to the Euler central charge.

hep-th↗

arXiv2012

Local Entropy Current in Higher Curvature Gravity and Rindler Hydrodynamics

In the hydrodynamic regime of field theories the entropy is upgraded to a local entropy current. The entropy current is constructed phenomenologically order by order in the derivative expansion by requiring that its divergence is non-negative. In the framework of the fluid/gravity correspondence, the entropy current of the fluid is mapped to a vector density associated with the event horizon of the dual geometry. In this work we consider the local horizon entropy current for higher-curvature gravitational theories proposed in arXiv:1202.2469, whose flux for stationary solutions is the Wald entropy. In non-stationary cases this definition contains ambiguities, associated with absence of a preferred timelike Killing vector. We argue that these ambiguities can be eliminated in general by choosing the vector that generates the subset of diffeomorphisms preserving a natural gauge condition on the bulk metric. We study a dynamical, perturbed Rindler horizon in Einstein-Gauss-Bonnet gravity setting and compute the bulk dual solution to second order in fluid gradients. We show that the corresponding unambiguous entropy current at second order has a manifestly non-negative divergence.

hep-th↗

arXiv2012

The Relativistic Rindler Hydrodynamics

We consider a (d+2)-dimensional class of Lorentzian geometries holographically dual to a relativistic fluid flow in (d+1) dimensions. The fluid is defined on a (d+1)-dimensional time-like surface which is embedded in the (d+2)-dimensional bulk space-time and equipped with a flat intrinsic metric. We find two types of geometries that are solutions to the vacuum Einstein equations: the Rindler metric and the Taub plane symmetric vacuum. These correspond to dual perfect fluids with vanishing and negative energy densities respectively. While the Rindler geometry is characterized by a causal horizon, the Taub geometry has a timelike naked singularity, indicating pathological behavior. We construct the Rindler hydrodynamics up to the second order in derivatives of the fluid variables and show the positivity of its entropy current divergence.

hep-th↗

arXiv2011

Holographic Screens and Transport Coefficients in the Fluid/Gravity Correspondence

We consider in the framework of the fluid/gravity correspondence the dynamics of hypersurfaces located in the holographic radial direction at r = r_0. We prove that these hypersurfaces evolve, to all orders in the derivative expansion and including all higher curvature corrections, according to the same hydrodynamics equations with identical transport coefficients. The analysis is carried out for normal fluids as well as for superfluids. Consequently, this proves the exactness of the bulk viscosity formula derived in arXiv:1103.1657 via the null horizon dynamics.

hep-th↗

arXiv2011

Higher Curvature Gravity and the Holographic fluid dual to flat spacetime

Recent works have demonstrated that one can construct a (d+2) dimensional solution of the vacuum Einstein equations that is dual to a (d+1) dimensional fluid satisfying the incompressible Navier-Stokes equations. In one important example, the fluid lives on a fixed timelike surface in the flat Rindler spacetime associated with an accelerated observer. In this paper, we show that the shear viscosity to entropy density ratio of the fluid takes the universal value 1/4πin a wide class of higher curvature generalizations to Einstein gravity. Unlike the fluid dual to asymptotically anti-de Sitter spacetimes, here the choice of gravitational dynamics only affects the second order transport coefficients. We explicitly calculate these in five-dimensional Einstein-Gauss-Bonnet gravity and discuss the implications of our results.

hep-th↗

arXiv2011

A Novel Formula for Bulk Viscosity from the Null Horizon Focusing Equation

The null horizon focusing equation is equivalent via the fluid/gravity correspondence to the entropy balance law of the fluid. Using this equation we derive a simple novel formula for the bulk viscosity of the fluid. The formula is expressed in terms of the dependence of scalar fields at the horizon on thermodynamic variables such as the entropy and charge densities. We apply the formula to three classes of gauge theory plasmas: non-conformal branes, perturbations of the N=4 supersymmetric Yang-Mills theory and holographic models of QCD, and discuss its range of applicability.

hep-th↗