Eisenhart lift for field theories

Kieran Finn, Sotirios Karamitsos, Apostolos Pilaftsis

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    Abstract

    We present the Eisenhart-lift formalism in which the dynamics of a system that evolves under the influence of a conservative force is equivalent to that of a free system embedded in a curved manifold with one additional generalized coordinate. As an illustrative example in classical mechanics, we apply this
    formalism to simple harmonic motion. We extend the Eisenhart lift to homogeneous field theories by adding one new field. Unlike an auxiliary field, this field is fully dynamical and is therefore termed fictitious. We show that the Noether symmetries of a theory with a potential are solutions of the Killing
    equations in the lifted field space. We generalize this approach to field theories in four and higher spacetime dimensions by virtue of a mixed vielbein that links the field space and spacetime. Possible applications of the extended Eisenhart-lift formalism including the gauge hierarchy problem and the initial conditions
    problem in inflation are briefly discussed.
    Original languageEnglish
    JournalPhysical Review D
    Volume98
    Issue number1
    Early online date27 Jul 2018
    DOIs
    Publication statusPublished - 2018

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