Cluster Transformations from Bipartite Field Theories

Abstract

Bipartite field theories (BFTs) are a new class of 4d N=1 quantum field theories defined by bipartite graphs on bordered Riemann surfaces. In this paper we derive, purely in terms of the gauge theory, the cluster transformations of face weights under square moves in the graph. In this context, we obtain them by connecting regular parametrizations of the master space of the associated BFTs. For BFTs on a disk, these transformations follow from the properties of coordinates in the Grassmannian. This represents a new addition to the list of combinatorial objects for the Grassmannian, such as matching and matroid polytopes, that have been shown to emerge from BFT dynamics.

v2: 19 pages, 6 figures. Accepted for publication in PRD

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• Dimer models and toric diagrams
• The Master Space of N=1 Gauge Theories
• Bipartite Field Theories: from D-Brane Probes to Scattering Amplitudes
• Network and Seiberg Duality
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Cited by in corpus (10)

• Bipartite Field Theories from D-Branes
• A Comprehensive Survey of Brane Tilings
• Scattering Amplitudes and Toric Geometry
• Cluster Algebras and the Positive Grassmannian
• Twin Theories, Polytope Mutations and Quivers for GTPs
• D-brane Instantons as Gauge Instantons in Orientifolds of Chiral Quiver Theories
• Bipartite field theories and D-brane instantons
• Anatomy of the Amplituhedron
• BFT${}_2$: a General Class of $2d$ $\mathcal{N}=(0,2)$ Theories, 3-Manifolds and Toric Geometry
• Consistent Dimer Models on Surfaces with Boundary