Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-01-29
J.Math.Phys. 36 (1995) 5284-5296
Physics
High Energy Physics
High Energy Physics - Theory
15pp, LaTex. Minor stylistic changes (title, abstract), to appear in the J. of Math.Physics
Scientific paper
10.1063/1.531262
We argue for the presence of a ${\bf Z}_2$ 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 ${\bf Z}_2$ homotopy group of mappings from the 2-dim. projective sphere ${\bf R}P^2$ into $SU(2n)/{\bf Z}_2$ and $SO(2n)/{\bf Z}_2$ 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 ${\bf Z}_2$ 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.
Axenides Minos
Johansen Andrei
Moller Jesper
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