Gribov-Zwanziger action in SU(2) Maximally Abelian Gauge with U(1)$_3$ Landau Gauge

Understand

We construct the local Gribov-Zwanziger action for SU(2) Euclidean Yang-Mills theories in the maximally Abelian (MA) gauge with U(1)$_3$ Landau gauge fixing based on the Zwanziger's work in the Landau gauge.

• By the restriction of the functional integral region to the Gribov region in the MA gauge, we give the nonlocal action.
• We localize the action with new fields and obtain the action with the shift of the new scalar fields, which has the terms, corresponding to the localized action of the horizon function in the MA gauge.
• The diagonal gluon propagator in the MA gauge at tree level behaves like the propagator from Gribov-Zwanziger action in the Landau gauge and shows the violation of Kallen-Lehmann representation.