Generating new dualities through the orbifold equivalence: a demonstration in ABJM and four-dimensional quivers

We show that the recently proposed large N equivalence between ABJM theories with Chern-Simons terms of different rank and level, U(N1)k1 × U(N1) − k1 and U(N2)k2 × U(N2)−k2, but the same value of N′ = N1k1 = N2k2, can be explained using planar equivalence in the mirror duals. The combination of S-dualities and orbifold equivalence can be applied to other cases as well, with very appealing results. As an example we show that two different quiver theories with k nodes can be easily shown to be Seiberg dual through the orbifold equivalence, but it requires order k2 steps to give a proof when Seiberg duality is performed node by node.