Gauge invariant Z_2 vortex vacuum textures and the SU(2) gluon condensate

TL;DR

This paper introduces a new gauge-invariant cooling method in SU(2) lattice gauge theory that reveals a Z(2) vortex vacuum texture, which may relate to the gluon condensate and differs from traditional P-vortex structures.

Contribution

It proposes a novel SO(3) cooling procedure that uncovers a gauge-invariant Z(2) vortex vacuum texture, distinct from P-vortices, and links it to the gluon condensate.

Findings

A new SO(3) cooling method isolates Z(2) vortex textures.

The vortex texture does not support the string tension.

The associated action density extrapolates smoothly to the continuum.

Abstract

For SU(2) lattice gauge theory, a new SO(3) cooling procedure is proposed which removes the SU(2)/Z(2) coset fields from the lattice configurations and reveals a Z(2) vortex vacuum texture different from the P-vortex content obtained in the maximal center gauge. Cooling can be restricted in a renormalization group invariant way by a parameter controlling the remaining SO(3) action density. A gauge invariant Z(2) vortex vacuum emerges asymptotically if cooling is not restricted. This ``vortex texture'' does not support the string tension or a finite part of it. The SU(2) action density associated with the new Z(2) vortex texture has a smooth extrapolation to the continuum limit. We propose an interpretation as a mass dimension four condensate related to the gluon condensate featuring in the operator product expansion.