Non-Relativistic Limits of Bosonic and Heterotic Double Field Theory

The known stringy non-relativistic (NR) limit of the universal NS-NS sector of supergravity has a finite Lagrangian due to non-trivial cancellations of divergent parts coming from the metric and the B-field. We demonstrate that in Double Field Theory (DFT) and generalised geometry these cancellations already happen at the level of the generalised metric, which is convergent in the limit c → ∞. On the level of bosonic DFT this implies that the NR limit can be taken before imposing the strong constraint and breaking the duality symmetry. At the (finite) leading order this reproduces the Non-Riemannian formulation of DFT. Assuming a convergent generalised metric for heterotic DFT, we derive a novel c-expansion for heterotic supergravity which is, by construction, O$(D,D)$-invariant.