Are all supergravity theories Yang-Mills squared?

TL;DR

This paper classifies certain four-dimensional $ ext{N}=2$ supergravity theories that can be constructed from Yang-Mills theories, identifying which can be obtained via a 'squared' construction and noting exceptions.

Contribution

It provides a symmetry-based classification of $ ext{N}=2$ supergravities arising from Yang-Mills theories, highlighting the conditions and exceptions for such constructions.

Findings

Most $ ext{N}=2$ supergravities with matter can be built from Yang-Mills theories.

Pure supergravity and the $T^3$ model are exceptions.

The classification is based on symmetry arguments.

Abstract

Using simple symmetry arguments we classify the ungauged $D=4$, $\mathcal{N}=2$ supergravity theories, coupled to both vector and hyper multiplets through homogeneous scalar manifolds, that can be built as the product of $\mathcal{N}=2$ and $\mathcal{N}=0$ matter-coupled Yang-Mills gauge theories. This includes all such supergravities with two isolated exceptions: pure supergravity and the $T^3$ model.