Eisenhart lift for higher derivative systems

Galajinsky, Anton; Masterov, Ivan

doi:10.1016/j.physletb.2016.11.059

Cited by 15 publications

(8 citation statements)

References 34 publications

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“…The lift establishes a correspondence between classical, non-relativistic motions in the presence of a scalar and vector potential and null geodesics in a higher dimensional spacetime, and extends to quantum mechanics relating the non-relativistic Schrödinger equation with the higher dimensional Klein-Gordon equation, and the Lévy-Leblond with the Dirac equation. The technique has been successfully used for several applications, as for example higher derivative systems [32] and non-relativistic holography [33][34][35], inspired by previous results in holography [36]; see [37] for a review of the associated geometry.…”

Section: Massless 4d Fermionsmentioning

confidence: 99%

Curvature-tuned electronic properties of bilayer graphene in an effective four-dimensional spacetime

2017

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We show that in AB stacked bilayer graphene low energy excitations around the semimetallic points are described by massless, four dimensional Dirac fermions. There is an effective reconstruction of the 4 dimensional spacetime, including in particular the dimension perpendicular to the sheet, that arises dynamically from the physical graphene sheet and the interactions experienced by the carriers. The effective spacetime is the Eisenhart-Duval lift of the dynamics experienced by Galilei invariant Lévy-Leblond spin 1 2 particles near the Dirac points. We find that changing the intrinsic curvature of the bilayer sheet induces a change in the energy level of the electronic bands, switching from a conducting regime for negative curvature to an insulating one when curvature is positive. In particular, curving graphene bilayers allows opening or closing the energy gap between conduction and valence bands, a key effect for electronic devices. Thus using curvature as a tunable parameter opens the way for the beginning of curvatronics in bilayer graphene.

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Section: Massless 4d Fermionsmentioning

confidence: 99%

Curvature-tuned electronic properties of bilayer graphene in an effective four-dimensional spacetime

2017

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“…It would be surprising if there were not some relation of these considerations to the present paper. Eisenhart-Duval lifts with two times have already been shown to arise for higher derivative systems [27]. If they can be isometrically embedded in higher dimensions even more time dimensions are likely to be required.…”

Section: Discussionmentioning

confidence: 99%

Lifting the Eisenhart-Duval Lift to a Minimal Brane

Gibbons

2020

Preprint

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The motion of a dynamical system on an n-dimensional configuration space may be regarded as the lightlike shadow of null geodsics moving in an (n+2) dimensional spacetime known as its Einsenhart-Duval lift. In this paper it is shown that if the configuration space is n-dimensional Euclidean space, and in the absence of magnetic type forces, the Eisenhart-Duval lift may be regarded as an (n + 1)-brane moving in a flat (n + 4)dimensional space with two times. If the Eisenhart-Duval lift is Ricci flat, then the (n+1)brane moves in such a way as to extremise its spacetime volume. A striking example is provided by the motion of N point particles moving in three-dimensional Euclidean space under the influence of their mutual gravitational attraction. Embedding with curved configuration space metrics and velocity dependent forces are also be constructed. Some of the issues arising from the two times are addressed.

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“…Our initial motivation for this research was to have a deeper understanding of the torsion condition. In nonrelativistic holography the bulk metrics are a pp-wave generalization of AdS spaces [38], clearly related to so called Eisenhart-Duval lift metrics [23,26,[39][40][41][42][43]. However, Eisenhart-Duval lift metrics have always been studied in the context of zero torsion.…”

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confidence: 99%

General theory of Galilean gravity

Cariglia

2018

Phys. Rev. D

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We obtain the complete theory of Newton-Cartan gravity in a curved spacetime by considering the large c limit of the vielbein formulation of General Relativity. Milne boosts originate from local Lorentzian transformations, and the special cases of torsionless and twistless torsional geometries are explained in the context of the larger locally Lorentzian theory. We write the action for Newton-Cartan fields in the first order Palatini formalism, and the large c limit of the Einstein equations. Finally, we obtain the generalised Eisenhart-Duval lift of the metric that plays an important role in non-relativistic holography.

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Eisenhart lift for higher derivative systems

Cited by 15 publications

References 34 publications

Curvature-tuned electronic properties of bilayer graphene in an effective four-dimensional spacetime

Curvature-tuned electronic properties of bilayer graphene in an effective four-dimensional spacetime

Lifting the Eisenhart-Duval Lift to a Minimal Brane

General theory of Galilean gravity

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