The fundamental interactions of nature are formulated in terms of fields classified by mass and spin. Two of the most successful theories, General Relativity (GR) and the Standard Model (SM), can be derived from fields of fixed mass and spin by imposing theoretical consistency conditions.
The SM contains well-understood interactions for fields with spin s<2, whereas local interacting theories with s>2 face fundamental obstacles, placing s=2 in a special position. Spin-2 fields are intrinsically linked to gravity, yet theories of interacting spin-2 fields remain comparatively unexplored. Lovelock’s theorem essentially establishes GR as the unique theory for a single massless spin-2 field, so it is natural to ask whether GR is part of a larger structure, as electromagnetism was later understood to sit within electroweak theory.
This may be relevant to open questions in gravitational physics, such as dark matter, dark energy, the Hubble tension, and, ultimately, quantum gravity. However, theories of interacting spin-2 fields are notoriously plagued by ghosts—pathological fields with negative kinetic energy—and requiring their absence severely restricts the allowed interactions.
In this talk, I will discuss multi-gravity theories, containing multiple interacting spin-2 fields, focusing on their theoretical consistency via the absence of ghosts.