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

TL;DR

This paper demonstrates how the replica sector in Yang--Mills theories can dynamically generate a Gribov horizon functional, leading to different infrared behaviors depending on the replica phase, and provides a microscopic mechanism for the Gribov scale emergence.

Contribution

It introduces a mechanism where the replica sector induces a Gribov horizon functional in Yang--Mills theories, connecting replica symmetry breaking to infrared dynamics.

Findings

Replica sector generates Gribov horizon functional.

Different phases yield distinct infrared behaviors.

Microscopic origin of the Gribov scale is identified.

Abstract

We show that the Serreau--Tissier (ST) replica sector can dynamically generate a Gribov--Zwanziger (GZ)--type horizon functional in Yang--Mills (YM) theories. After integrating out the replica superfields, the expansion of the determinant of the Faddeev--Popov (FP) operator in the regulator $\zeta$ produces, at linear order in $\zeta$, a nonlocal kernel with the same color and Lorentz structure as the Gribov horizon functional, thereby defining an induced Gribov scale. Depending on the replica phase selected by the dynamics, the ST sector yields either (i) a local Curci--Ferrari (CF) screening mass (replica-symmetric phase) or (ii) an induced horizon-like interaction (replica-broken phase). In the latter case, the resulting BRST-invariant local formulation leads to a tree-level gluon propagator of the refined Gribov-Zwanziger (RGZ) decoupling type, whereas in the former it reduces to the massive FP/CF form, avoiding double counting of infrared scales by construction. A superspace derivation confirms that the induced horizon term originates from the ST superdeterminant, providing a microscopic mechanism for the emergence of the Gribov scale within the replica framework.