Goldstino couplings to matter

Abstract

A nonlinearly realized supersymmetric action describing the invariant couplings of the Goldstino to matter is constructed. Using the Akulov-Volkov Lagrangian, any operator can be made part of a supersymmetric-invariant action. Of particular interest are interaction terms which include the product of the Akulov-Volkov Lagrangian with the ordinary matter Lagrangian as well as the coupling of the product of the covariant derivative of the Goldstino field to the matter supersymmetry current. The latter is the lowest dimensional operator linear in the Goldstino field. A Goldstino Goldberger-Treiman relation is established and shown to be satisfied by the effective action.