Testing the nonperturbative orbifold conjecture

We discuss Strassler’s hypothesis of matching nonperturbative effects in orbifold pairs of gauge theories which are perturbatively planar equivalent. One of the examples considered is the parent $\mathcal{N}=1\mathrm{}\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ supersymmetric Yang-Mills theory and its nonsupersymmetric orbifold daughter. We apply two strategies allowing us to study nonperturbative effects: (i) low-energy theorems and (ii) putting the theory on small-size $T^4$ or $R^3\times S^1.$ Then both the parent and daughter theories are weakly coupled and amenable to quasiclassical treatment. In all cases our consideration yields a mismatch between the parent and daughter theories. Thus, regretfully, we present evidence against Strassler’s hypothesis. We discuss in passing a brane picture related to our consideration.