Non-Riemannian gravity actions from double field theory

TL;DR

This paper uses double field theory to construct and clarify actions for non-Riemannian gravitational theories, including Torsional Newton-Cartan, Carrollian, and String Newton-Cartan gravities, aiding understanding of quantum gravity and non-relativistic systems.

Contribution

It employs double field theory to derive and clarify actions for various non-Riemannian gravity theories, resolving previous ambiguities and enabling better comparison with existing results.

Findings

Derived actions for Torsional Newton-Cartan, Carrollian, and String Newton-Cartan gravities.

Embedded these theories within double field theory framework.

Compared new actions with existing literature results.

Abstract

Non-Riemannian gravitational theories suggest alternative avenues to understand properties of quantum gravity and provide a concrete setting to study condensed matter systems with non-relativistic symmetry. Derivation of an action principle for these theories generally proved challenging for various reasons. In this technical note, we employ the formulation of double field theory to construct actions for a variety of such theories. This formulation helps removing ambiguities in the corresponding equations of motion. In particular, we embed Torsional Newton-Cartan gravity, Carrollian gravity and String Newton-Cartan gravity in double field theory, derive their actions and compare with the previously obtained results in literature.