Interactions of chiral two-forms

Two issues regarding the interactions of the chiral two-forms are reviewed. First, the problem of constructing Lorentz-invariant self-couplings of a single chiral two-form is investigated in the light of the Dirac-Schwinger condition on the energy-momentum tensor commutation relations. We show how the Perry-Schwarz condition follows from the Dirac-Schwinger criterion and point out that consistency of the gravitational coupling is automatic. Secondly, we study the possible local deformations of chiral two-forms. This problem reduces to the study of the local BRST cohomological group at ghost number zero. We proof that the only consistent deformations of a system of free chiral two-forms are (up to redefinitions) deformations that do not modify the abelian gauge symmetries of the free theory. The consequence of this result for a system consisting of a number of parallel M5-branes is explained.