UV Constraints on Massive Spinning Particles: Lessons from the Gravitino

Understand

Self-interacting massive particles with spin $\geq 1$ unavoidably violate unitarity; the question is at what scale.

• For spin-$1$ the strong coupling scale (at which perturbative unitarity is lost) cannot be raised by any finite tuning of the interactions, while for spin-$2$ there exists a special tuning of the Wilson coefficients which can raise this scale (and enjoys numerous special properties such as ghost-freedom).
• Here, we fill in the missing piece by describing how the self-interactions of a massive spin-$3/2$ field, or "massive gravitino", become strongly coupled at high energies.
• We show that while several different structures appear in the leading order potential, the strong coupling scale cannot be raised (in the absence of additional fields).