Emergent Gribov horizon kernel from replica symmetry breaking in Yang--Mills theories

We show that, in the replica-broken sector of the Serreau–Tissier (ST) gauge fixing, the expansion of the replica determinant in the regulator $\zeta$ induces a nonlocal bilinear gluonic kernel with the same color and Lorentz structure as the quadratic part of the BRST-invariant Gribov horizon functional. This establishes an effective leading-order correspondence with the refined Gribov-Zwanziger (RGZ) horizon sector, rather than a reconstruction of the full nonlinear functional $H(A^h)$. The induced scale satisfies ${\gamma }_{\mathrm{i}\mathrm{n}\mathrm{d}}^4\propto \zeta$ at leading order, up to scheme-dependent normalization and higher-order corrections. Depending on the replica phase, the ST sector yields either a local Curci–Ferrari (CF) screening mass or an induced RGZ-type horizon kernel, avoiding double counting of infrared scales.