Non-Riemannian isometries from double field theory

TL;DR

This paper investigates isometries in non-Riemannian geometries using double field theory, revealing infinite-dimensional symmetry algebras and their relation to non-relativistic string symmetries, including supersymmetric extensions.

Contribution

It demonstrates that non-Riemannian backgrounds admit infinite-dimensional isometry algebras within double field theory, connecting these to known string symmetries and extending to supersymmetric cases.

Findings

Infinite-dimensional isometry algebra including supertranslations

Correspondence with Gomis-Ooguri non-relativistic string symmetries

Supersymmetric extension with arbitrary dependence on non-Riemannian directions

Abstract

We explore the notion of isometries in non-Riemannian geometries. Such geometries include and generalise the backgrounds of non-relativistic string theory, and they can be naturally described using the formalism of double field theory. Adopting this approach, we first solve the corresponding Killing equations for constant flat non-Riemannian backgrounds and show that they admit an infinite-dimensional algebra of isometries which includes a particular type of supertranslations. These symmetries correspond to known worldsheet Noether symmetries of the Gomis-Ooguri non-relativistic string, which we now interpret as isometries of its non-Riemannian doubled background. We further consider the extension to supersymmetric double field theory and show that the corresponding Killing spinors can depend arbitrarily on the non-Riemannian directions, leading to "supersupersymmetries" that square to supertranslations.