From Exceptional Field Theory to Heterotic Double Field Theory via K3

TL;DR

This paper demonstrates deriving heterotic double field theory from exceptional field theory through supersymmetry breaking, using an $ ext{SU}(2)$-structure reduction, and explores its relation to M-theory on K3 and heterotic string duality.

Contribution

It introduces a method to obtain heterotic double field theory from exceptional field theory via $ ext{SU}(2)$-structure reduction, linking M-theory on K3 to heterotic string theory.

Findings

Reduction on $ ext{SU}(2)$-structure breaks half of the supersymmetry.

The gauge group is determined by the embedding tensor of the reduction.

The approach connects M-theory on K3 with heterotic string on $T^3$.

Abstract

In this paper we show how to obtain the heterotic double field theory from exceptional field theory by breaking half of the supersymmetry. We focus on the $\mathrm{SL}(5)$ exceptional field theory and show that when the extended space contains a generalised $\mathrm{SU}(2)$-structure manifold one can define a reduction to obtain the heterotic $\mathrm{SO}(3,n)$ double field theory. In this picture, the reduction on the $\mathrm{SU}(2)$-structure breaks half of the supersymmetry of the exceptional field theory and the gauge group of the heterotic double field theory is given by the embedding tensor of the reduction used. Finally, we study the example of a consistent truncation of M-theory on K3 and recover the duality with the heterotic string on $T^3$. This suggests that the extended space can be made sense of even in the case of non-toroidal compactifications.