Anti-BRST symmetry and background field method

We show that the requirement that a SU(N) Yang-Mills action (gauge fixed in a linear covariant gauge) is invariant under both the Becchi-Rouet-Stora-Tyutin (BRST) symmetry as well as the corresponding anti-BRST symmetry, automatically implies that the theory is quantized in the (linear covariant) background field method (BFM) gauge. Thus, the BFM and its associated background Ward identity naturally emerge from anti-BRST invariance of the theory and need not be introduced as an ad hoc gauge fixing procedure. Treating ghosts and antighosts on an equal footing, as required by a BRST-anti-BRST invariant formulation of the theory, gives also rise to a local antighost equation that together with the local ghost equation completely resolves the algebraic structure of the ghost sector for any value of the gauge fixing parameter. We finally prove that the background fields are stationary points of the background effective action obtained when the quantum fields are integrated out.