摘要 : Mirror Symmetry for a large class of three dimensional \( \mathcal{N} = 4 \) supersymmetric gauge theories has a natural explanation in terms of M-theory compactified on a product of ALE spaces. A pair of such mirror duals can be ... 展开 Mirror Symmetry for a large class of three dimensional \( \mathcal{N} = 4 \) supersymmetric gauge theories has a natural explanation in terms of M-theory compactified on a product of ALE spaces. A pair of such mirror duals can be described as two different deformations of the eleven-dimensional supergravity background \( \mathcal{M} = {\mathbb{R}^{2,1}} \times {\text{AL}}{{\text{E}}_1} \times {\text{AL}}{{\text{E}}_2} \), to which they flow in the deep IR. Using the A − D − E classification of ALE spaces, we present a neat way to catalogue dual quiver gauge theories that arise in this fashion. In addition to the well-known examples studied in [1, 2], this procedure leads to new sets of dual theories. For a certain subset of dual theories which arise from the aforementioned M-theory background with an A-type ALE1 and a D-type ALE2, we verify the duality explicitly by a computation of partition functions of the theories on S 3, using localization techniques. We derive the relevant mirror map and discuss its agreement with predictions from the Type IIB brane construction for these theories. 收起