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

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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' =N₁ k₁=N₂ k₂, 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.