A supersymmetric Lagrangian for fermionic fields with mass dimension one

We present the derivation of a supersymmetric model for fermionic fields with integer-valued mass dimension based on a general superfield with one free spinor index. First, we develop a formalism based on a general superfield with one free spinor index. Then, we systematically derive all associated chiral and antichiral superfields up to third order in covariant derivatives. Using this formalism we are able to construct a supersymmetric on-shell Lagrangian that contains a kinetic term for the fermionic fields with mass dimension one. We then derive the corresponding on-shell supercurrent and succeed in formulating a consistent second quantization for the component fields. Finally, we present our result for a supersymmetric Hamiltonian. As the Lagrangian is by construction supersymmetric and the Hamiltonian was derived from the Lagrangian using supersymmetry algebra the Hamiltonian must be positive definite.

DEFORMATION OF SCHILD STRING

We attempt to construct new superstring actions with a D-plet of Majorana fermions [Formula: see text], where ℬ is the D-dimensional space–time index and A is the two-dimensional spinor index, by deforming the Schild action. As a result, we propose three kinds of actions: the first is invariant under N=1 (the worldsheet) supersymmetry transformation and the area-preserving diffeomorphism. The second contains the Yukawa type interaction. The last possesses some nonlocality because of bilinear terms of [Formula: see text]. The reasons why completing a Schild type superstring action with [Formula: see text] is difficult are finally discussed.