Non-Relativistic Limits of Bosonic and Heterotic Double Field Theory

TL;DR

This paper investigates non-relativistic limits of Double Field Theory and heterotic supergravity, showing that cancellations occur at the level of the generalised metric, allowing the limit to be taken before solving the strong constraint.

Contribution

It introduces a new approach to non-relativistic limits in DFT and heterotic theories by expanding the generalised metric, revealing finite limits and extending to non-Abelian gauge fields.

Findings

The generalised metric remains finite in the non-relativistic limit.

The approach reproduces non-Riemannian DFT at leading order.

A novel c-expansion for heterotic supergravity is derived.

Abstract

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 $c \rightarrow \infty$, implying that the NR limit can be imposed before solving the strong constraint. We present the $c$-expansion of the generalised metric, which reproduces the Non-Riemannian formulation of DFT at the (finite) leading order, and the $c$-expansion of the generalised frame, which contains divergences. We also extend this approach to the non-Abelian gauge field of Heterotic DFT assuming a convergent expansion for the O$(D,D+n)$ generalised metric. From this proposal, we derive a novel $c$-expansion for the bosonic part of the heterotic supergravity which is, by construction, compatible with O$(D,D)$-symmetry.