The fields are the -valued connection form A, -valued scalar field with fermionic statistics, b and c and a -valued scalar field with bosonic statistics B. c deals with the gauge transformations whereas b and B deal with the gauge fixings. There actually are some subtleties associated with the gauge fixing due to Gribov ambiguities but they will not be covered here.
The text describes a theoretical model involving two scalar fields: one fermionic (with c) and one bosonic (with b and B). Gauge transformations are handled by 'c', while 'b' and 'B' deal with gauge fixings.  Gribov ambiguities in gauge fixing are mentioned but not discussed further.