Abstract
Newton-Cartan geometry has played a central role in recent discussions of non-relativistic holography and condensed matter systems. Although the conformal transformation in non-relativistic holography can be easily rephrased in Newton-Cartan geometry, we show that it requires a nontrivial procedure to get the consistent form of anisotropic disformal transformation in this geometry. Furthermore, as an application of the newly obtained disformal transformation, we use it to induce a new geometry.
Highlights
Newton–Cartan geometry (NCG) was proposed by Élie Cartan as a geometrical description for Newtonian gravity in the spirit of general relativity [1,2]
Via conformal rescaling, the conformal NCG could be induced from the original geometry
A key procedure to induce a new geometry is to rewrite the original geometrical variables with new variables obtained through disformal transformation
Summary
Newton–Cartan geometry (NCG) was proposed by Élie Cartan as a geometrical description for Newtonian gravity in the spirit of general relativity [1,2] (see [3]). Except for the obvious applications in gravity theories, a possible non-relativistic version of the disformal transformation may have implications for the nonrelativistic holography given the power and utility of conformal transformations in this area With these observations in mind, together with all the important facts about NCG, some questions can be naturally proposed:. A sound knowledge about the non-relativistic disformal transformation and disformal extension of NCG is helpful for constructing disformally invariant field theories as well as gravity theories, which have the potential to enrich the investigations broaden the horizons of condensed matter theory and holography All these considerations constitute the motivation for the present work.
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