Towards M2-brane Theories for Generic Toric Singularities

Abstract

We construct several examples of (2+1) dimensional N=2 supersymmetric Chern-Simons theories, whose moduli space is given by non-compact toric Calabi-Yau four-folds, which are not derivable from any (3+1) dimensional CFT. One such example is the gauge theory associated with the cone over Q^{111}. For several examples, we explicitly confirm the matter content, superpotential interactions and RG flows suggested by crystal models. Our results provide additional support to the idea that crystal models are relevant for describing the structure of these CFTs.

33 pages, 16 figures

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• A Stringy Origin of M2 Brane Chern-Simons Theories
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• AdS_4/CFT_3 duals from M2-branes at hypersurface singularities and their deformations
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• Infrared Stability of N=2 Chern-Simons Matter Theories
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• Superconformal index for large N quiver Chern-Simons theories
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• Integrability on the Master Space
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• Probing the Space of Toric Quiver Theories
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• Dimer algebras, ghor algebras, and cyclic contractions
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• Probing Non-Toric Geometry with Rotating Membranes
• BPS $M2$-branes in $Ad{S}_4\times Q^{1,1,1}$ Dual to Loop Operators
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• Quiver Chern-Simons theories and 3-algebra orbifolds
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