We discuss BRST and anti-BRST transformations for an Abelian antisymmetric gauge field in 4D and find that, in order for them to anticommute,
we have to impose a condition on the auxiliary fields. This condition is similar to the Curci–Ferrari condition for the 4D non-Abelian 1-form
gauge theories and represents a consistency requirement. We interpret it as a signal that our Abelian 2-form gauge field theory is based on gerbes.
To support this interpretation we discuss, in particular, the case of the 1-gerbe for our present field theory and write the relevant equations and symmetry transformations for 2-gerbes.
