BRST, anti-BRST and their geometry.

We continue the comparison between the field theoretical and geometrical approaches to the gauge field theories of various types, by deriving their Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST transformation properties and comparing them with the geometrical properties of the bundles and gerbes. In particular, we provide the geometrical interpretation of the so-called Curci–Ferrari conditions that are invoked for the absolute anticommutativity of the BRST and anti-BRST symmetry transformations in the context of non-Abelian one-form gauge theories as well as the Abelian gauge theory that incorporates a two-form gauge field. We also carry out the explicit construction of the three-form gauge fields and compare it with the geometry of 2-gerbes.