Gravity Beyond a Single Metric Ghost-free interactions of spin-2 fields

by Joakim Flinckman (Stockholm University)

Friday 15 May 2026, 13:00 → 16:00 Europe/Stockholm

FB42 (AlbaNova Main Building)

Abstract
The mathematical formulations of the fundamental interactions in nature are all expressed in terms of fields classified by
their mass and spin. The structure of two of the most successful theories in physics, General Relativity and the Standard
Model of particle physics, can both be derived more or less uniquely from fields with fixed mass and spin, guided by
theoretical consistency conditions. The Standard Model contains well-understood interactions of particles with spins less
than two, while theories involving spins higher than two are generally problematic. Theories of spin-2 fields are much less
explored, and in particular, any consistent multiplet structure, crucial for the Standard Model, is practically unknown.
Even without considering multiplet structures, classical theories with interacting spin-2 fields generically propagate
additional pathological fields, so-called Boulware–Deser ghosts, rendering such theories physically unacceptable. Until
recently, only a non-derivative interaction between two spin-2 fields, called bimetric theory, had been proven consistent.
While the bimetric interaction can to some extent be trivially extended to more than two fields, genuine ghost-free multifield
interactions have remained elusive.
In this thesis, we derive necessary conditions on ghost-free non-derivative interactions between multiple spin-2 fields.
With a suitable parametrisation of the fields, the ghost mode can be isolated, allowing one to derive necessary conditions
for it to be non-propagating. These conditions essentially determine the form of the interaction potential uniquely, up to
a set of free constant parameters. The admissible class contains all previously known ghost-free theories, but is not itself
ghost-free in general. Imposing an additional necessary condition for ghost-freedom on these parameters further restricts
the interaction to the Hassan–Schmidt–May theory and trivial extensions thereof. Thus, much as for the lower-spin theories
in the Standard Model, the requirement of theoretical consistency, here the absence of ghosts, essentially singles out the
admissible theory. We then show that this theory possesses the full set of constraints needed to eliminate all ghost modes,
establishing it as the most general known ghost-free multi-gravity interaction. Finally, we derive the mass spectrum, finding
one massless and multiple massive spin-2 fields with a non-tachyonic spectrum.