The ${\mathcal{N}}_3=3\to {\mathcal{N}}_3=4$ enhancement of Super Chern-Simons theories in $D=3$, Calabi HyperKähler metrics and M2-branes on the $\mathcal{C}({\mathrm{N}}^{0,1,0})$ conifold

Abstract

Considering matter coupled supersymmetric Chern-Simons theories in three dimensions we extend the Gaiotto-Witten mechanism of supersymmetry enhancement ${\mathcal{N}}_3=3\to {\mathcal{N}}_3=4$ from the case where the hypermultiplets span a flat HyperKähler 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 HyperKähler metrics compatible with the enhancement condition is provided by the Calabi metrics on $T^{\star }{\mathbb{P}}^n$. In this list we find, for $n=2$ the resolution of the metric cone on ${\mathrm{N}}^{0,1,0}$ which is the unique homogeneous Sasaki Einstein 7-manifold leading to an ${\mathcal{N}}_4=3$ 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 HyperKähler manifolds in terms of gauged fixed supergroup Chern Simons theories. The relevant supergroup is in this case $\mathrm{SU}(3|N)$ where $\mathrm{SU}(3)$ is the flavor group and $\mathrm{U}(\mathrm{N})$ is the color group.

arXiv comment2 figures, 64 pages

References in corpus (19)

• Comments on Multiple M2-branes
• Janus Configurations, Chern-Simons Couplings, And The Theta-Angle in N=4 Super Yang-Mills Theory
• On Mirror Symmetry in Three Dimensional Abelian Gauge Theories
• A supermatrix model for N=6 super Chern-Simons-matter theory
• Spectrum of Type IIB Supergravity on AdS_5 x T^{11}: Predictions on N = 1 SCFT's
• On N=8 Supergravity on $Ad{S}_5$ and N=4 Superconformal Yang-Mills theory
• 3D superconformal theories from Sasakian seven-manifolds: new nontrivial evidences for AdS_4/CFT_3
• Notes on adding D6 branes wrapping RP3 in AdS4 x CP3
• Conformal Maxwell theory as a singleton field theory on AdS_5, IIB three-branes and duality
• Hyper-Kahler Calabi Metrics, L^2 Harmonic Forms, Resolved M2-branes, and AdS_4/CFT_3 Correspondence
• 3-branes on spaces with R x S^2 x S^3 topology
• M-theory on AdS_4xM^{111}: the complete Osp(2|4)xSU(3)xSU(2) spectrum from harmonic analysis
• Rings of short N=3 superfields in three dimensions and M-theory on AdS_4 x N^{0,1,0}
• The structure of N=3 multiplets in AdS_4 and the complete Osp(3|4) X SU(3) spectrum of M-theory on AdS_4 X N^{010}
• Chern-Simons-Rozansky-Witten topological field theory
• Osp(N|4) supermultiplets as conformal superfields on \partial AdS_4 and the generic form of N=2, D=3 gauge theories
• The Gauge/Gravity Theory of Blown up Four Cycles
• The complete N=3 Kaluza Klein spectrum of 11D supergravity on AdS_4 x N^{010}
• Conformal Symmetry of Supergravities in AdS spaces