Toric Fano varieties and Chern-Simons quivers

Abstract

In favourable cases the low energy dynamics of a stack of M2-branes at a toric Calabi-Yau fourfold singularity can be described by an N=2 supersymmetric Chern-Simons quiver theory, but there still does not exists an "inverse algorithm" going from the toric data of the CY_4 to the CS quiver. We make progress in that direction by deriving CS quiver theories for M2-branes probing cones over a large class of geometries Ypq(B_4), which are S^3/Z_p bundles over toric Fano varieties B_4. We rely on the type IIA understanding of CS quivers, giving a firm string theory footing to our CS theories. In particular we give a derivation of some previously conjectured CS quivers in the case B_4= CP^1*CP^1, as field theories dual to M-theory backgrounds with nontrivial torsion G_4 fluxes.

92 pages and many figures. v2: section 7.3 on quivers with equal ranks expanded. v3: added a reference

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Cited by in corpus (14)

• Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective
• Symmetry TFTs for 3d QFTs from M-theory
• The supersymmetric NUTs and bolts of holography
• Cluster algebras from dualities of 2d N=(2,2) quiver gauge theories
• Rank-two 5d SCFTs from M-theory at isolated toric singularities: a systematic study
• The moduli spaces of $3d$ $\mathcal{N}\ge 2$ Chern-Simons gauge theories and their Hilbert series
• Holographic RG flows in N=3 Chern-Simons-Matter theory from N=3 4D gauged supergravity
• Wilson loops and the geometry of matrix models in AdS_4/CFT_3
• Double Handled Brane Tilings
• The Backreacted Kähler Geometry of Wrapped Branes
• Operator Counting for N=2 Chern-Simons Gauge Theories with Chiral-like Matter Fields
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• Spin(7) duality for N=1 CS-matter theories
• Semiclassics of three-dimensional SCFTs from holography