Lorentz-non-invariant counter-terms in QCD in a general axial gauge

It is shown in the context of a pure Yang-Mills theory that the solution of the Slavnov-Taylor identities in a general axial gauge admits counter-terms which may or may not be Lorentz invariant. It follows from the background field method that these counter-terms must be gauge invariant. The Lorentz-non-invariant counter-terms appear already at the one-loop level and depend both on the gauge parameter α and the non-covariant vector n_ω.