New Directions in Bipartite Field Theories

Abstract

We perform a detailed investigation of Bipartite Field Theories (BFTs), a general class of 4d N=1 gauge theories which are defined by bipartite graphs. This class of theories is considerably expanded by identifying a new way of assigning gauge symmetries to graphs. A new procedure is introduced in order to determine the toric Calabi-Yau moduli spaces of BFTs. For graphs on a disk, we show that the matroid polytope for the corresponding cell in the Grassmannian coincides with the toric diagram of the BFT moduli space. A systematic BFT prescription for determining graph reductions is presented. We illustrate our ideas in infinite classes of BFTs and introduce various operations for generating new theories from existing ones. Particular emphasis is given to theories associated to non-planar graphs.

70+2 pages. v2: minor clarifications

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Cited by in corpus (24)

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• A slow review of the AGT correspondence
• Chiral theories of class S
• Unoriented Quivers with Flavour
• Bipartite Field Theories from D-Branes
• A Comprehensive Survey of Brane Tilings
• The Geometry of On-Shell Diagrams
• Scattering Amplitudes and Toric Geometry
• Double Handled Brane Tilings
• Cluster Transformations from Bipartite Field Theories
• Twin Theories, Polytope Mutations and Quivers for GTPs
• Calabi-Yau Varieties: from Quiver Representations to Dessins d'Enfants
• D-brane Instantons as Gauge Instantons in Orientifolds of Chiral Quiver Theories
• Bipartite field theories and D-brane instantons
• Non-Planar On-Shell Diagrams
• Gauge Theories, Tessellations & Riemann Surfaces
• BFT${}_2$: a General Class of $2d$ $\mathcal{N}=(0,2)$ Theories, 3-Manifolds and Toric Geometry
• Consistent Dimer Models on Surfaces with Boundary
• Hilbert Series of Bipartite Field Theories
• Bipartite Graphs, On-Shell Diagrams, and Bipartite Field Theories: a Computational Package in Mathematica
• Brane Tilings as On-shell Diagrams