Massless vierbein spin-5/2 fields and hypergravity

The authors present and analyze the physical content of new gauge invariant actions for pure massless spin-5/2 fields represented by nonsymmetric vierbein like variables. The consistency requirements for gravitational coupling are analyzed. In the Minkowski case these lead to very stringent restrictions on the solutions, such as vanishing Weyl tensor. In the Euclidean regime, self-dual systems, i.e. half-flat gravitational and pure helicity matter fields are allowed, due to vanishing of the fermionic stress tensor for pure helicity states. (Auth.)