Are all supergravity theories Yang-Mills squared?

TL;DR

The paper classifies ungauged $D=4$, $\mathcal{N}=2$ supergravities with homogeneous scalar manifolds that can be constructed as the square of a Yang-Mills theory, using a left $\mathcal{N}_L=2$ and right $\mathcal{N}_R=0$ gauge-factor product. By organizing the vector and hyper multiplet sectors into projective special Kähler and quaternionic manifolds, the authors identify all symmetric coset cases (generic Jordan, magic, minimally coupled) and the non-symmetric families, highlighting symmetry enhancements and the role of a spectator field in the squaring construction. With two notable exceptions—pure $\mathcal{N}=2$ supergravity and the $T^3$ model—the full set of homogeneous theories arises from this Yang-Mills squaring, and the hypermultiplet sector often requires a diagonal identification of $SU(2)$ factors for non-symmetric cases. The work links squaring to the BCJ double-copy program and suggests future work on non-homogeneous manifolds and $\mathcal{N}=1$ theories, as well as a BCJ-consistency check for the Right gauge theory factors. Overall, it strengthens the understanding of gravity/gauge-factor relations and clarifies which $\mathcal{N}=2$ theories admit a Yang-Mills origin via a structured, symmetry-driven squaring procedure.

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.