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(N-1)(k1) x U(N-1)(-k1) and U(N-2)(k2) x U(N-2)(-k2), but the same value of N' = N(1)k(1) = N(2)k(2), 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 k(2) steps to give a proof when Seiberg duality is performed node by node.