  We show that a powerful Slavnov-Taylor (ST) identity exists for the Effective
Field Theory (EFT) of the Color Glass Condensate (CGC), allowing to control by
purely algebraic means the full dependence on the background fields of the fast
gluon modes, as well as the correlators of the quantum fluctuations of the
classical gluon source. We use this formalism to study the change of the
background fast modes (in the Coulomb gauge), induced by the quantum
corrections of the semi-fast gluons. We establish the evolution equation for
the EFT of the CGC, which points towards an algebraic derivation of the JIMWLK
equation. Being based on symmetry-arguments only, the approach can be used to
extend the analysis to arbitrary gauges and to higher orders in the
perturbation expansion of the EFT.
