A worldsheet supersymmetric Newton-Cartan string

Understand

We construct a (locally) supersymmetric worldsheet action for a string in a non-relativistic Newton-Cartan background.

• We do this using a doubled string action, which describes the target space geometry in an $O(D,D)$ covariant manner using a doubled metric and doubled vielbeins.
• By adopting different parametrisations of these doubled background fields, we can describe both relativistic and non-relativistic geometries.
• We focus on the torsional Newton-Cartan geometry which can be obtained by null duality/reduction (such null duality is particularly simple for us to implement).