Disformal transformation in Newton-Cartan geometry

TL;DR

This paper explores how disformal transformations can be consistently implemented within Newton-Cartan geometry and demonstrates their application in generating new geometric structures relevant to non-relativistic holography.

Contribution

It introduces a novel formulation of anisotropic disformal transformations in Newton-Cartan geometry and applies it to construct new geometric configurations.

Findings

Disformal transformations in Newton-Cartan geometry require a nontrivial procedure.

A consistent anisotropic disformal transformation is formulated.

New geometries are generated using the disformal transformation.

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.