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.
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