The N3=3 → N3=4 enhancement of super Chern-Simons theories in D=3, Calabi HyperKahler metrics and M2-branes on the l (N0,1,0) conifold

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 (TPn)-P-star. In this list we find, for n = 2 the resolution of the metric cone on N-0,N-1,N-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. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This study investigates matter coupled supersymmetric Chern-Simons theories in three dimensions, extending the Gaiotto-Witten mechanism from flat HyperKahler manifolds to curved ones, and deriving precise conditions for supersymmetry enhancement. An infinite class of HyperKahler metrics compatible with the enhancement condition is provided by Calabi metrics on (CPn)-CP*, with specific examples leading to unique homogeneous Sasaki-Einstein 7-manifolds in the context of M-theory compactification.