High-energy QCD evolution from BRST symmetry

We show that the (gauge-fixed) classical action of the Color Glass Condensate is invariant under a suitable Becchi–Rouet–Stora–Tyutin symmetry, which holds after the gluon modes are split into their fast, semi-fast, and soft components, according to the longitudinal momenta they carry. This entails the existence of a corresponding Slavnov–Taylor identity which in turn strongly constrains the effective field theory arising when integrating out the semi-fast modes. Specifically, we prove that this identity guarantees the gauge invariance of the resulting effective theory. In addition, we use it to demonstrate that the integration over the semi-fast modes does not deform the classical Yang–Mills equations of motion, thus validating a key assumption in the usual procedure adopted when deriving the renormalization group equation governing the evolution with energy of the effective theory. As far as the latter are concerned, we finally prove that its functional form is common, and it is determined by symmetry arguments alone. The formal properties of these equations valid in different regimes and/or approximations (e.g., the JIMWLK equation and its BFKL limit) can be therefore derived in a unified setting within this algebraic approach.