How to halve maximal supergravity

TL;DR

This paper details the process of truncating four-dimensional maximal supergravity to half-maximal supergravity, explicitly deriving the necessary constraints on the embedding tensors that define the theories.

Contribution

It explicitly derives the linear and quadratic constraints on embedding tensors for truncation from N=8 to N=4 supergravity, including a brane interpretation.

Findings

Derived the linear constraint on N=8 theories for N=4 truncation.

Determined the additional quadratic constraints for N=4 from N=8.

Commented on brane interpretation as tadpole conditions.

Abstract

We work out the truncation from maximal to half-maximal supergravity in four dimensions. In particular, we determine the explicit constraints on the embedding tensors of both theories. These tensors specify the complete theories, including gauge groups and scalar potentials. Firstly, we find the linear constraint on N=8 theories to allow for a truncation to N=4. Secondly, we determine the additional N=4 quadratic constraints following from N=8. Finally, we comment on a brane interpretation as tadpole conditions for the latter.