Action formulation of a chiral strictly massless spin-5/2 theory

Determine whether the anti-self-duality constraint for a chiral, strictly massless spin-5/2 theory on de Sitter space can be incorporated consistently at the level of an action functional, with the aim of obtaining a unitary quantum field theory.

Background

The authors propose a possible way to avoid the indefinite norm problem of the Hermitian de Sitter action by restricting to a chiral theory whose field strength is anti-self-dual. This approach is motivated by the analogous discussion for the strictly massless gravitino.

The anti-self-duality condition is currently imposed only on shell. Whether an action can implement this condition remains unresolved, so the proposed chiral route to a unitary de Sitter theory is incomplete.

References

A possible way out in order to achieve a unitary QFT on dS$_4$ is to consider a chiral, strictly massless spin-$\tfrac{5}{2}$ theory, where the field strength is anti-self-dual, as explained in for the gravitino. However, the anti-self-duality constraint is imposed on-shell and its incorporation at the level of the action is unclear;

— Sphere path integrals for fermionic gauge fields  (2609.19275 - Baracco et al., 16 Sep 2026) in Section 2, “Lorentzian formulation,” subsection “Lorentzian formulation”