Abstract Considering matter coupled supersymmetric Chern–Simons theories in three dimensions we extend the Gaiotto-Witten mechanism of supersymmetry enhancement N 3 = 3 → N 3 = 4 from the case where the hypermultiplets span a flat HyperKahler manifold to that where they live on a curved one. We derive the precise conditions of this enhancement in terms of generalized Gaiotto-Witten identities to be satisfied by the tri-holomorphic moment maps. An infinite class of HyperKahler metrics compatible with the enhancement condition is provided by the Calabi metrics on T ⋆ P n . In this list we find, for n = 2 the resolution of the metric cone on N 0,1,0 which is the unique homogeneous Sasaki Einstein 7-manifold leading to an N 4 = 3 compactification of M-theory. This leads to challenging perspectives for the discovery of new relations between the enhancement mechanism in D = 3 , the geometry of M2-brane solutions and also for the dual description of super Chern Simons theories on curved HyperKahler manifolds in terms of gauged fixed supergroup Chern Simons theories.

中文翻译：

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N3=3→N3=4 在 D=3、Calabi HyperKähler 度量和 C(N0,1,0) 分形上的 M2-膜中对超级陈-西蒙斯理论的增强

摘要 考虑三个维度的物质耦合超对称陈-西蒙斯理论，我们将超对称增强 N 3 = 3 → N 3 = 4 的 Gaiotto-Witten 机制从超多重态跨越平坦的 HyperKahler 流形的情况扩展到它们生活在弯曲的流形上的情况。一。我们根据三全纯矩图满足的广义 Gaiotto-Witten 恒等式推导出这种增强的精确条件。与增强条件兼容的无限类 HyperKahler 度量由 T ⋆ P n 上的 Calabi 度量提供。在这个列表中，我们发现，对于 n = 2，公制锥在 N 0,1,0 上的分辨率是唯一齐次 Sasaki Einstein 7-流形，导致 M 理论的 N 4 = 3 紧化。