BRST, anti-BRST and gerbes

Understand

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.