Gauge invariance and background field formalism in the exact renormalisation group

We discuss gauge symmetry and Ward–Takahashi identities for Wilsonian flows in pure Yang–Mills theories. The background field formalism is used for the construction of a gauge invariant effective action. The symmetries of the effective action under gauge transformations for both the gauge field and the auxiliary background field are separately evaluated. We examine how the symmetry properties of the full theory are restored in the limit where the cut-off is removed.