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arXiv · 2012.07766

Non-Riemannian isometries from double field theory

Chris D. A. Blair·Gerben Oling·Jeong-Hyuck Park
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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.

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Chris D. A. Blair, Gerben Oling, Jeong-Hyuck Park. 2021-03-24. Non-Riemannian isometries from double field theory. https://doi.org/10.1007/jhep04(2021)072

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