Deformations of chiral two-forms in six dimensions

Motivated by a system consisting of a number of parallel M5-branes, we study possible local deformations of chiral two-forms in six dimensions. Working to first order in the coupling constant, this reduces to the study of the local BRST cohomological group at ghost number zero. We obtain an exhaustive list of all possible deformations. None of them allows for a satisfactory formulation of the M5-branes system leading to the conclusion that no local field theory can describe such a system.