Two-loop ghost-antighost condensation for SU(2) Yang-Mills theories in the Maximal Abelian Gauge

TL;DR

This paper investigates ghost-antighost condensation in SU(2) Yang-Mills theories within the Maximal Abelian Gauge, deriving a two-loop effective potential and analyzing the conditions under which condensation occurs without mass generation.

Contribution

It provides an analytical derivation of the two-loop effective potential for ghost-antighost condensation in this gauge, extending previous one-loop analyses.

Findings

Ghost-antighost pairing persists at two loops.

No mass generation occurs with the chosen propagator ansatz.

Condensation does not disrupt the one-loop pairing in this framework.

Abstract

In the framework of the formalism of Cornwall et all. for composite operators I study the ghost-antighost condensation in SU(2) Yang-Mills theories quantized in the Maximal Abelian Gauge and I derive analytically a condensating effective potential at two ghost loops. I find that in this approximation the one loop pairing ghost-antighost is not destroyed but no mass is generated if the ansatz for the propagator suggested by the tree level Hubbard-Stratonovich transformations is used.