arXiv subjects

Jelle Hartong

Publications and source records attributed to Jelle Hartong.

At least 55 records · Page 3Linked to original sources

arXiv2017

Holographic Reconstruction of 3D Flat Space-Time

We study asymptotically flat space-times in 3 dimensions for Einstein gravity near future null infinity and show that the boundary is described by Carrollian geometry. This is used to add sources to the BMS gauge corresponding to a non-trivial boundary metric in the sense of Carrollian geometry. We then solve the Einstein equations in a derivative expansion and derive a general set of equations that take the form of Ward identities. Next, it is shown that there is a well-posed variational problem at future null infinity without the need to add any boundary term. By varying the on-shell action with respect to the metric data of the boundary Carrollian geometry we are able to define a boundary energy-momentum tensor at future null infinity. We show that its diffeomorphism Ward identity is compatible with Einstein's equations. There is another Ward identity that states that the energy flux vanishes. It is this fact that is responsible for the enhancement of global symmetries to the full BMS$_3$ algebra when we are dealing with constant boundary sources. Using a notion of generalized conformal boundary Killing vector we can construct all conserved BMS$_3$ currents from the boundary energy-momentum tensor.

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arXiv2016

Gauge Coupling Field, Currents, Anomalies and N=1 Super-Yang-Mills Effective Actions

Working with a gauge coupling field in a linear superfield, we construct effective Lagrangians for N=1 super-Yang-Mills theory fully compatible with the expected all-order behaviour or physical quantities. Using the one-loop dependence on its ultraviolet cutoff and anomaly matching or cancellation of R and dilatation anomalies, we obtain the Wilsonian effective Lagrangian. With similar anomaly matching or cancellation methods, we derive the effective action for gaugino condensates, as a function of the real coupling field. Both effective actions lead to a derivation of the NSVZ beta function from algebraic arguments only. The extension of results to N=2 theories or to matter systems is briefly considered. The main tool for the discussion of anomalies is a generic supercurrent structure with 16_B+16_F operators (the S multiplet), which we derive using superspace identities and field equations for a fully general gauge theory Lagrangian with the linear gauge coupling superfield, and with various U(1)_R currents. As a byproduct, we show under which conditions the S multiplet can be improved to contain the Callan-Coleman-Jackiw energy-momentum tensor whose trace measures the breaking of scale invariance.

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arXiv2016

Symmetries and Couplings of Non-Relativistic Electrodynamics

We examine three versions of non-relativistic electrodynamics, known as the electric and magnetic limit theories of Maxwell's equations and Galilean electrodynamics (GED) which is the off-shell non-relativistic limit of Maxwell plus a free scalar field. For each of these three cases we study the couplings to non-relativistic dynamical charged matter (point particles and charged complex scalars). The GED theory contains besides the electric and magnetic potentials a so-called mass potential making the mass parameter a local function. The electric and magnetic limit theories can be coupled to twistless torsional Newton-Cartan geometry while GED can be coupled to an arbitrary torsional Newton-Cartan background. The global symmetries of the electric and magnetic limit theories on flat space consist in any dimension of the infinite dimensional Galilean conformal algebra and a $U(1)$ current algebra. For the on-shell GED theory this symmetry is reduced but still infinite dimensional, while off-shell only the Galilei algebra plus two dilatations remain. Hence one can scale time and space independently, allowing Lifshitz scale symmetries for any value of the critical exponent $z$.

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arXiv2016

Torsional Newton-Cartan Geometry from the Noether Procedure

We apply the Noether procedure for gauging space-time symmetries to theories with Galilean symmetries, analyzing both massless and massive (Bargmann) realizations. It is shown that at the linearized level the Noether procedure gives rise to (linearized) torsional Newton-Cartan geometry. In the case of Bargmann theories the Newton-Cartan form $M_μ$ couples to the conserved mass current. We show that even in the case of theories with massless Galilean symmetries it is necessary to introduce the form $M_μ$ and that it couples to a topological current. Further, we show that the Noether procedure naturally gives rise to a distinguished affine (Christoffel type) connection that is linear in $M_μ$ and torsionful. As an application of these techniques we study the coupling of Galilean electrodynamics to TNC geometry at the linearized level.

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arXiv2016

Lifshitz Hydrodynamics from Lifshitz Black Branes with Linear Momentum

We construct a new class of 4-dimensional z=2 Lifshitz black branes that have a nonzero linear momentum. These are solutions of an Einstein-Proca-dilaton model that can be obtained by Scherk-Schwarz circle reduction of AdS_5 gravity coupled to a free real scalar field. The boundary of a bulk Lifshitz space-time is a Newton-Cartan geometry. We show that the fluid dual to the moving Lifshitz black brane leads to a novel form of Lifshitz hydrodynamics on a Newton-Cartan space-time. Since the linear momentum of the black brane cannot be obtained by a boost transformation the velocity of the fluid or rather, by boundary rotational invariance, its magnitude plays the role of a chemical potential. The conjugate dual variable is mass density. The Lifshitz perfect fluid can be thought of as arising from a Schroedinger perfect fluid with broken particle number symmetry.

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arXiv2016

Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity

We show that certain three-dimensional Horava-Lifshitz gravity theories can be written as Chern-Simons gauge theories on various non-relativistic algebras. The algebras are specific extensions of the Bargmann, Newton-Hooke and Schroedinger algebra each of which has the Galilean algebra as a subalgebra. To show this we employ the fact that Horava-Lifshitz gravity corresponds to dynamical Newton-Cartan geometry. In particular, the extended Bargmann (Newton-Hooke) Chern-Simons theory corresponds to projectable Horava-Lifshitz gravity with a local U(1) gauge symmetry without (with) a cosmological constant. Moreover we identify an extended Schroedinger algebra containing 3 extra generators that are central with respect to the subalgebra of Galilean boosts, momenta and rotations, for which the Chern-Simons theory gives rise to a novel version of non-projectable conformal Horava-Lifshitz gravity that we refer to as Schroedinger gravity. This theory has a z=2 Lifshitz geometry as a vacuum solution and thus provides a new framework to study Lifshitz holography.

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arXiv2015

Gauging the Carroll Algebra and Ultra-Relativistic Gravity

It is well known that the geometrical framework of Riemannian geometry that underlies general relativity and its torsionful extension to Riemann-Cartan geometry can be obtained from a procedure known as gauging the Poincare algebra. Recently it has been shown that gauging the centrally extended Galilei algebra, known as the Bargmann algebra, leads to a geometrical framework that when made dynamical gives rise to Horava-Lifshitz gravity. Here we consider the case where we contract the Poincare algebra by sending the speed of light to zero leading to the Carroll algebra. We show how this algebra can be gauged and we construct the most general affine connection leading to the geometry of so-called Carrollian space-times. Carrollian space-times appear for example as the geometry on null hypersurfaces in a Lorentzian space-time of one dimension higher. We also construct theories of ultra-relativistic (Carrollian) gravity in 2+1 dimensions with dynamical exponent z<1 including cases that have anisotropic Weyl invariance for z=0.

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arXiv2015

Horava-Lifshitz Gravity From Dynamical Newton-Cartan Geometry

Recently it has been established that torsional Newton-Cartan (TNC) geometry is the appropriate geometrical framework to which non-relativistic field theories couple. We show that when these geometries are made dynamical they give rise to Horava-Lifshitz (HL) gravity. Projectable HL gravity corresponds to dynamical Newton-Cartan (NC) geometry without torsion and non-projectable HL gravity corresponds to dynamical NC geometry with twistless torsion (hypersurface orthogonal foliation). We build a precise dictionary relating all fields (including the scalar khronon), their transformations and other properties in both HL gravity and dynamical TNC geometry. We use TNC invariance to construct the effective action for dynamical twistless torsional Newton-Cartan geometries in 2+1 dimensions for dynamical exponent 1<z\le 2 and demonstrate that this exactly agrees with the most general forms of the HL actions constructed in the literature. Further, we identify the origin of the U(1) symmetry observed by Horava and Melby-Thompson as coming from the Bargmann extension of the local Galilean algebra that acts on the tangent space to TNC geometries. We argue that TNC geometry, which is manifestly diffeomorphism covariant, is a natural geometrical framework underlying HL gravity and discuss some of its implications.

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arXiv2015

Lifshitz Space-Times for Schroedinger Holography

We show that asymptotically locally Lifshitz space-times are holographically dual to field theories that exhibit Schroedinger invariance. This involves a complete identification of the sources, which describe torsional Newton-Cartan geometry on the boundary and transform under the Schroedinger algebra. We furthermore identify the dual vevs from which we define and construct the boundary energy-momentum tensor and mass current and show that these obey Ward identities that are organized by the Schroedinger algebra. We also point out that even though the energy flux has scaling dimension larger than z+2, it can be expressed in terms of computable vev/source pairs.

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arXiv2015

Schroedinger Invariance from Lifshitz Isometries in Holography and Field Theory

We study non-relativistic field theory coupled to a torsional Newton-Cartan geometry both directly as well as holographically. The latter involves gravity on asymptotically locally Lifshitz space-times. We define an energy-momentum tensor and a mass current and study the relation between conserved currents and conformal Killing vectors for flat Newton-Cartan backgrounds. It is shown that flat NC space-time realizes two copies of the Lifshitz algebra that together form a Schroedinger algebra (without the central element). We show why the Schroedinger scalar model has both copies as symmetries and the Lifshitz scalar model only one. Finally we discuss the holographic dual of this phenomenon by showing that the bulk Lifshitz space-time realizes the same two copies of the Lifshitz algebra.

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arXiv2015

Field Theory on Newton-Cartan Backgrounds and Symmetries of the Lifshitz Vacuum

Holography for Lifshitz space-times corresponds to dual field theories on a fixed torsional Newton-Cartan (TNC) background. We examine the coupling of non-relativistic field theories to TNC backgrounds and uncover a novel mechanism by which a global U(1) can become local. This involves the TNC vector $M_μ$ which sources a particle number current, and which for flat NC space-time satisfies $M_μ=\partial_μM$ with a Schroedinger symmetry realized on $M$. We discuss various toy model field theories on flat NC space-time for which the new mechanism leads to extra global space-time symmetries beyond the generic Lifshitz symmetry, allowing for an enhancement to Schroedinger symmetry. On the holographic side, the source $M$ also appears in the Lifshitz vacuum with exactly the same properties as for flat NC space-time. In particular, the bulk diffeomorphisms that preserve the boundary conditions realize a Schroedinger algebra on $M$, allowing for a conserved particle number current. Finally, we present a probe action for a complex scalar field on the Lifshitz vacuum, which exhibits Schroedinger invariance in the same manner as seen in the field theory models.

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arXiv2014

Torsional Newton-Cartan Geometry and the Schrödinger Algebra

We show that by gauging the Schrödinger algebra with critical exponent $z$ and imposing suitable curvature constraints, that make diffeomorphisms equivalent to time and space translations, one obtains a geometric structure known as (twistless) torsional Newton-Cartan geometry (TTNC). This is a version of torsional Newton-Cartan geometry (TNC) in which the timelike vielbein $τ_μ$ must be hypersurface orthogonal. For $z=2$ this version of TTNC geometry is very closely related to the one appearing in holographic duals of $z=2$ Lifshitz space-times based on Einstein gravity coupled to massive vector fields in the bulk. For $z\neq 2$ there is however an extra degree of freedom $b_0$ that does not appear in the holographic setup. We show that the result of the gauging procedure can be extended to include a Stückelberg scalar $χ$ that shifts under the particle number generator of the Schrödinger algebra, as well as an extra special conformal symmetry that allows one to gauge away $b_0$. The resulting version of TTNC geometry is the one that appears in the holographic setup. This shows that Schrödinger symmetries play a crucial role in holography for Lifshitz space-times and that in fact the entire boundary geometry is dictated by local Schrödinger invariance. Finally we show how to extend the formalism to generic torsional Newton-Cartan geometries by relaxing the hypersurface orthogonality condition for the timelike vielbein $τ_μ$.

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arXiv2014

Particle Number and 3D Schroedinger Holography

We define a class of space-times that we call asymptotically locally Schroedinger space-times. We consider these space-times in 3 dimensions, in which case they are also known as null warped AdS. The boundary conditions are formulated in terms of a specific frame field decomposition of the metric which contains two parts: an asymptotically locally AdS metric and a product of a lightlike frame field with itself. Asymptotically we say that the lightlike frame field is proportional to the particle number generator N regardless of whether N is an asymptotic Killing vector or not. We consider 3-dimensional AlSch space-times that are solutions of the massive vector model. We show that there is no universal Fefferman-Graham (FG) type expansion for the most general solution to the equations of motion. We show that this is intimately connected with the special role played by particle number. Fefferman-Graham type expansions are recovered if we supplement the equations of motion with suitably chosen constraints. We consider three examples. 1). The massive vector field is null everywhere. The solution in this case is exact as the FG series terminates and has N as a null Killing vector. 2). N is a Killing vector (but not necessarily null). 3). N is null everywhere (but not necessarily Killing). The latter case contains the first examples of solutions that break particle number, either on the boundary directly or only in the bulk. Finally, we comment on the implications for the problem of holographic renormalization for asymptotically locally Schroedinger space-times.

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arXiv2014

Torsional Newton-Cartan Geometry and Lifshitz Holography

We obtain the Lifshitz UV completion in a specific model for z=2 Lifshitz geometries. We use a vielbein formalism which enables identification of all the sources as leading components of well-chosen bulk fields. We show that the geometry induced from the bulk onto the boundary is a novel extension of Newton-Cartan geometry with a specific torsion tensor. We explicitly compute all the vevs including the boundary stress-energy tensor and their Ward identities. After using local symmetries/Ward identities the system exhibits 6+6 sources and vevs. The FG expansion exhibits, however, an additional free function which is related to an irrelevant operator whose source has been turned off. We show that this is related to a second UV completion.

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arXiv2013

Boundary Stress-Energy Tensor and Newton-Cartan Geometry in Lifshitz Holography

For a specific action supporting z=2 Lifshitz geometries we identify the Lifshitz UV completion by solving for the most general solution near the Lifshitz boundary. We identify all the sources as leading components of bulk fields which requires a vielbein formalism. This includes two linear combinations of the bulk gauge field and timelike vielbein where one asymptotes to the boundary timelike vielbein and the other to the boundary gauge field. The geometry induced from the bulk onto the boundary is a novel extension of Newton-Cartan geometry that we call torsional Newton-Cartan (TNC) geometry. There is a constraint on the sources but its pairing with a Ward identity allows one to reduce the variation of the on-shell action to unconstrained sources. We compute all the vevs along with their Ward identities and derive conditions for the boundary theory to admit conserved currents obtained by contracting the boundary stress-energy tensor with a TNC analogue of a conformal Killing vector. We also obtain the anisotropic Weyl anomaly that takes the form of a Horava-Lifshitz action defined on a TNC geometry. The Fefferman-Graham expansion contains a free function that does not appear in the variation of the on-shell action. We show that this is related to an irrelevant deformation that selects between two different UV completions.

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arXiv2013

Holographic Models for Theories with Hyperscaling Violation

We study in detail a variety of gravitational toy models for hyperscaling-violating Lifshitz (hvLif) space-times. These space-times have been recently explored as holographic dual models for condensed matter systems. We start by considering a model of gravity coupled to a massive vector field and a dilaton with a potential. This model supports the full class of hvLif space-times and special attention is given to the particular values of the scaling exponents appearing in certain non-Fermi liquids. We study linearized perturbations in this model, and consider probe fields whose interactions mimic those of the perturbations. The resulting equations of motion for the probe fields are invariant under the Lifshitz scaling. We derive Breitenlohner-Freedman-type bounds for these new probe fields. For the cases of interest the hvLif space-times have curvature invariants that blow up in the UV. We study the problem of constructing models in which the hvLif space-time can have an AdS or Lifshitz UV completion. We also analyze reductions of Schroedinger space-times and reductions of waves on extremal (intersecting) branes, accompanied by transverse space reductions, that are solutions to supergravity-like theories, exploring the allowed parameter range of the hvLif scaling exponents.

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arXiv2012

On Supercurrent Superfields and Fayet-Iliopoulos Terms in N=1 Gauge Theories

We revisit the supermultiplet structure of Noether currents for N=1 supersymmetric gauge theories. Using superfield identities and the field equations we show how to derive a superfield equation for the divergences of the Noether currents in terms of the supercurrent and anomaly superfields containing 16_B+16_F components. We refer to this as the natural supercurrent structure as it is invariant under all local symmetries of the theory. It corresponds to the S-multiplet of Komargodski and Seiberg. We clarify the on/off-shell nature of the currents appearing in this multiplet and we study in detail the effect of specific improvement transformations leading to 1) a Ferrara-Zumino multiplet and to 2) a multiplet containing the new improved energy-momentum tensor of Callan, Coleman and Jackiw. Our methods also apply to supersymmetric gauge theories with a Fayet-Iliopoulos term. We construct the natural supercurrent multiplet for such a theory and show how to improve this to a formally gauge-invariant Ferrara-Zumino multiplet by introducing a non-dynamical chiral superfield S to ensure superfield gauge invariance. Finally we study the coupling of this theory to supergravity and show that S remains non-dynamical if the theory is R-symmetric and that S becomes propagating if the theory is not R-symmetric, leading to non-minimal 16_B+16_F supergravity.

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arXiv2012

From D3-Branes to Lifshitz Space-Times

We present a simple embedding of a z=2 Lifshitz space-time into type IIB supergravity. This is obtained by considering a stack of D3-branes in type IIB supergravity and deforming the world-volume by a plane wave. The plane wave is sourced by the type IIB axion. The superposition of the plane wave and the D3-branes is 1/4 BPS. The near horizon geometry of this configuration is a 5-dimensional z=0 Schroedinger space-time times a 5-sphere. This geometry is also 1/4 BPS. Upon compactification along the direction in which the wave is traveling the 5-dimensional z=0 Schroedinger space-time reduces to a 4-dimensional z=2 Lifshitz space-time. The compactification is such that the circle is small for weakly coupled type IIB string theory. This reduction breaks the supersymmetries. Further, we propose a general method to construct analytic z=2 Lifshitz black brane solutions. The method is based on deforming 5-dimensional AdS black strings by an axion wave and reducing to 4-dimensions. We illustrate this method with an example.

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