Nonperturbative ghost dynamics in the maximal Abelian gauge

TL;DR

This paper develops an effective potential for ghost condensates in the maximal Abelian gauge, revealing spontaneous symmetry breaking and unphysical Goldstone modes, contributing to understanding nonperturbative gauge dynamics.

Contribution

It introduces a novel effective potential for ghost condensates in the maximal Abelian gauge, highlighting spontaneous symmetry breaking and the nature of Goldstone modes.

Findings

Ghost condensate acts as an order parameter for symmetry breaking.

Spontaneous symmetry breaking lowers vacuum energy.

Goldstone mode associated with the condensate is unphysical.

Abstract

We construct the effective potential for the ghost condensate <f^{abi}\bar{c}^a c^b> in the maximal Abelian gauge. This condensate is an order parameter for a global continuous symmetry, which is spontaneously broken since a nonvanishing value of <f^{abi}\bar{c}^a c^b> lowers the vacuum energy. The associated Goldstone mode turns out to be unphysical.