Self-interacting chiral p-forms in higher dimensions

There exists no natural variational principle for the dynamics of abelian p-form potentials with self-dual field strengths, also called chiral p-forms. Relying on the PST method, we establish the general consistency condition for a Lagrangian to describe a Lorentz invariant self-interacting chiral 2n-form in 4n+2 dimensions. For a generic n, we determine a canonical solution of this condition for a quartic interaction Lagrangian of the 2n-form, and prove that for the four-form in ten dimensions this interaction is unique. It generalizes the corresponding Born-Infeld-like interaction of a chiral two-form in six dimensions. We verify that under a dimensional reduction on a torus, this interaction Lagrangian reduces to a combination of the two recently constructed SO(2)-duality invariant quartic interactions for abelian three-form potentials in eight dimensions. The potential relevance of our method for the type IIB superstring effective action is discussed.