  In the large N_c limit, some apparently different gauge theories turn out to
be equivalent due to large N_c orbifold equivalence. We use effective field
theory techniques to explore orbifold equivalence, focusing on the specific
case of a recently discovered relation between an SO(2N_c) gauge theory and
QCD. The equivalence to QCD has been argued to hold at finite baryon chemical
potential, \mu_B, so long as one deforms the SO(2N_c) theory by certain
"double-trace" terms. The deformed SO(2N_c) theory can be studied without a
sign problem in the chiral limit, in contrast to SU(N_c) QCD at finite \mu_B.
The purpose of the double-trace deformation in the SO(2N_c) theory is to
prevent baryon number symmetry from breaking spontaneously at finite density,
which is necessary for the equivalence to large N_c QCD to be valid. The
effective field theory analysis presented here clarifies the physical
significance of double-trace deformations, and strongly supports the proposed
equivalence between the deformed SO(2N_c) theory and large N_c QCD at finite
density.
