On the Z₂ Monopole of Spin(10) Gauge Theories

An "expanded" description is introduced to examine the spinor-monopole identification proposed by Strassler for four-dimensional $\cal N$ = 1 supersymmetric Spin(10) gauge theories with matter in F vector and N spinor representations. It is shown that a Z_2 monopole in the "expanded" theory is associated with massive spinors of the Spin(10) theory. For N=2, two spinor case, we confirm this identification by matching the transformation properties of the two theories under SU(2) flavor symmetry. However, for N $\ge$ 3, the transformation properties are not matched between the spinors and the monopole. This disagreement might be due to the fact that the SU(N) flavor symmetry of the Spin(10) theory is partially realized as an SU(2) symmetry in the "expanded" theory.