We study the SU(3) gluon propagator in renormalizable $R_xi$ gauges implemented on a symmetric lattice with a total volume of (3.25 fm)$^4$ for values of the guage fixing parameter up to $xi=0.5$. As expected, the longitudinal gluon dressing function
stays constant at its tree-level value $xi$. Similar to the Landau gauge, the transverse $R_xi$ gauge gluon propagator saturates at a non-vanishing value in the deep infrared for all values of $xi$ studied. We compare with very recent continuum studies and perform a simple analysis of the found saturation with a dynamically generated effective gluon mass.
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.
