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

TL;DR

This paper demonstrates how orbifold equivalence and S-duality can explain large N equivalences between ABJM theories and relate different quiver theories through Seiberg duality, simplifying complex proofs.

Contribution

It introduces a novel explanation for large N equivalences in ABJM theories using planar mirror duals and orbifold equivalence, and applies this to relate quiver theories via Seiberg duality.

Findings

Large N equivalence explained via mirror duals and orbifold methods

Orbifold equivalence simplifies proving Seiberg duality between quivers

Method reduces proof complexity from order k^2 to a more manageable process

Abstract

We show that the recently proposed large $N$ equivalence between ABJM theories with Chern-Simons terms of different rank and level, U(N_1)_{k_1}\times U(N_1)_{-k_1} and U(N_2)_{k_2}\times U(N_2)_{-k_2}, 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.