Phases of M2-brane Theories

Abstract

We investigate different toric phases of 2+1 dimensional quiver gauge theories arising from M2-branes probing toric Calabi-Yau 4 folds. A brane tiling for each toric phase is presented. We apply the 'forward algorithm' to obtain the toric data of the mesonic moduli space of vacua and exhibit the equivalence between the vacua of different toric phases of a given singularity. The structures of the Master space, the mesonic moduli space, and the baryonic moduli space are examined in detail. We compute the Hilbert series and use them to verify the toric dualities between different phases. The Hilbert series, R-charges, and generators of the mesonic moduli space are matched between toric phases.

60 pages, 28 figures, 6 tables. v2: minor corrections

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• Comments on 3d Seiberg-like dualities
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• Large $N$ matrix models for 3d $\mathcal{N}=2$ theories: twisted index, free energy and black holes
• M2-branes on Orbifolds of the Cone over Q^{1,1,1}
• Quantum moduli space of Chern-Simons quivers, wrapped D6-branes and AdS4/CFT3
• Hilbert Series for Moduli Spaces of Two Instantons
• N=2 solutions of massive type IIA and their Chern-Simons duals
• The Large N Limit of Toric Chern-Simons Matter Theories and Their Duals
• Membranes with Topological Charge and AdS4/CFT3 Correspondence
• ABJM Mirrors and a Duality of Dualities
• Baryonic symmetries and M5 branes in the AdS_4/CFT_3 correspondence
• On the Classification of Brane Tilings
• Higgsing M2-brane Theories
• Symmetries of Abelian Orbifolds
• 3D Seiberg-like Dualities and M2 Branes
• Toric Fano varieties and Chern-Simons quivers
• Free Energy vs Sasaki-Einstein Volume for Infinite Families of M2-Brane Theories
• Refined Checks and Exact Dualities in Three Dimensions
• Z-extremization and F-theorem in Chern-Simons matter theories
• New 3d $\mathcal{N}=2$ SCFT's with $N^{3/2}$ scaling
• Wilson loops and the geometry of matrix models in AdS_4/CFT_3
• The Hilbert series of U/SU SQCD and Toeplitz Determinants
• N=1 Chern-Simons theories, orientifolds and Spin(7) cones
• (Un)Higgsing the M2-brane
• Z Extremization in Chiral-Like Chern Simons Theories
• Chern-Simons: Fano and Calabi-Yau
• On the exact R charge for N=2 CS theories
• On nonsupersymmetric $\BC^4/\BZ_N$, tachyons, terminal singularities and flips
• M5 spikes and operators in the HVZ membrane theory
• Moduli space of supersymmetric QCD in the Veneziano limit
• Probing the Space of Toric Quiver Theories
• R-symmetry and supersymmetry breaking in 3D WZ models
• Spin(7) duality for N=1 CS-matter theories
• Is toric duality a Seiberg-like duality in (2+1)-d ?
• Inverse algorithm and M2-brane theories
• The ADHM-like Constructions for Instantons on CP^2 and Three Dimensional Gauge Theories
• Aspects of the moduli space of instantons on $\mathbb{C}{P}^2$ and its orbifolds
• Partial resolution of complex cones over Fano $\mathcal{B}$
• Large-$N$ Free Energy of Chiral $\mathcal{N}=2$ Chern-Simons-Matter Theories
• Brane Resolution Through Fibration
• Hilbert Series of Bipartite Field Theories
• Embedding and partial resolution of complex cones over Fano threefolds
• Aspects of ABJM orbifolds with discrete torsion
• On the structure of quadrilateral brane tilings