Comments on Equations of Motion for Pure Spinors in Even Dimensions

Abstract

A Berkovits type action for pure spinors in even dimensions is considered. The equations of motion for pure spinors are investigated by using explicit parameterizations which solve the pure spinor constraints. For general interactions, the equations of motions are shown to be modified from the naive ones. The extra terms contain a particular projector. If the interactions are restricted to the ``ghost number'' u(1) and the Lorentz so(p,q) current couplings, the action has a large ``gauge symmetry''. In this case, in some ``gauges'', the extra terms vanish and the equations of motion for the pure spinors retain the naive form even if the pure spinor constraints are taken into account.