  A summary is reported on our previous publications about four-dimensional N=1
supersymmetric Spin(10) gauge theory with chiral superfields in the spinor and
vector representations in the non-Abelian Coulomb phase. Carrying out the
method of a-maximization, we studied decoupling operators in the infrared and
the renormalization flow of the theory. We also give a brief review on the
non-Abelian Coulomb phase of the theory after recalling the unitarity bound and
the a-maximization procedure in four-dimensional conformal field theory. This
is a review article invited to International Journal of Modern Physics A.
