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, μ 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 μ 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.