A ${\mathbf{Z}}_2$ Structure in the Configuration Space of Yang-Mills Theories

Abstract

We argue for the presence of a ${\mathbf{Z}}_2$ topological structure in the space of static gauge-Higgs field configurations of $SU(2n)$ and $SO(2n)$ Yang-Mills theories. We rigorously prove the existence of a ${\mathbf{Z}}_2$ homotopy group of mappings from the 2-dim. projective sphere $\mathbf{R}{P}^2$ into $SU(2n)/{\mathbf{Z}}_2$ and $SO(2n)/{\mathbf{Z}}_2$ Lie groups respectively. Consequently the symmetric phase of these theories admits infinite surfaces of odd-parity static and unstable gauge field configurations which divide into two disconnected sectors with integer Chern-Simons numbers $n$ and $n+1/2$ respectively. Such a ${\mathbf{Z}}_2$ structure persists in the Higgs phase of the above theories and accounts for the existence of $CS=1/2$ odd-parity saddle point solutions to the field equations which correspond to spontaneous symmetry breaking mass scales.

15pp, LaTex. Minor stylistic changes (title, abstract), to appear in the J. of Math.Physics

References in corpus (2)

• Progress in Electroweak Baryogenesis
• Topological Classification of Odd-Parity Sphaleron Deformations

Cited by in corpus (3)

• Electroweak Baryon Number Non-Conservation in the Early Universe and in High Energy Collisions
• $Z_2$ as the Topological Origin of B+L Violation in the Hot Electroweak Theory
• A ${\mathbf{Z}}_2$ Classification for 2D Fermion Level Crossing