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

Abstract

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 ${\gamma }_{\mathrm{ind}}^4\propto \zeta$ 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.

22 pages, 1 table. Version accepted for publication in The European Physical Journal C

References in corpus (7)

• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• Gribov no-pole condition, Zwanziger horizon function, Kugo-Ojima confinement criterion, boundary conditions, BRST breaking and all that
• Non-perturbative aspects of Euclidean Yang-Mills theories in linear covariant gauges: Nielsen identities and a BRST invariant two-point correlation function
• An all order renormalizable Refined-Gribov-Zwanziger model with BRST invariant fermionic horizon function in linear covariant gauges
• Towards a unified viewpoint of Gribov--Zwanziger and Serreau--Tissier gauge fixing
• Gauge-covariant stochastic neural fields: Stability and finite-width effects