Comments on chiral p-forms

Two issues regarding chiral p-forms are addressed. First, we investigate th e topological conditions on spacetime under which the action for a nonchira l p-form can be split as the sum of the actions for two chiral p-forms, one of each chirality. When these conditions are not met, we exhibit explicitl y the extra topological degrees of freedom and their couplings to the chira l modes. Second, we study the problem of constructing Lorentz-invariant sel f-couplings of a chiral p-form in the light of the Dirac-Schwinger conditio n on the energy-momentum tensor commutation relations. We show how the Perr y-Schwarz condition follows from the Dirac-Schwinger criterion and point ou t that consistency of the gravitational coupling is automatic.