Self-interactions of the massive spin-2 supermultiplet

Develop self-interactions for the massive spin-2 supermultiplet in order to analyze the massless limit of the supersymmetric extension of bigravity and determine how the no-go results for multiple massless supergravities apply.

Background

The paper constructs cubic interactions between massless N=1 supergravity and a massive (2,3/2,3/2,1) supermultiplet, viewing the resulting theory as a possible supersymmetric extension of bigravity. The construction is fixed at the cubic level by gauge-invariant massive-field descriptions, unfolded-equation deformations, and restrictions to the minimum number of derivatives.

The conclusion notes that the model has a nonsingular massless limit and recalls no-go theorems for interacting massless spin-2 fields and for multiple massless supergravities. To investigate the corresponding issue in the supersymmetric setting, the massive spin-2 supermultiplet must be supplemented with self-interactions; constructing those interactions is left unresolved.

References

But similar no-go results also hold for the massless multi supergravities as well . So it would be interesting and important to analyse what happens in the supersymmetric case. To do this, we have to add self-interactions for the massive spin-2 supermultiplet (see e.g. ), but we leave this task for the future.

— Massive spin-2 supermultiplet and supergravity  (2608.19896 - Zinoviev, 20 Aug 2026) in Conclusion