Twin Theories, Polytope Mutations and Quivers for GTPs
arXiv:2302.10951 · doi:10.1007/JHEP07(2023)034
Abstract
We propose a unified perspective on two sets of objects that usually arise in the study of bipartite field theories. Each of the sets consists of a polytope, or equivalently a toric Calabi-Yau, and a quiver theory. We refer to the two sets of objects as original and twin. In the simplest cases, the two sides of the correspondence are connected by the graph operation known as untwisting. The democratic treatment that we advocate raises new questions regarding the connections between these objects, some of which we explore. With this motivation in mind, we establish a correspondence between the mutations of the original polytope and the twin quiver. This leads us to propose that non-toric twin quivers are naturally associated to generalized toric polygons (GTPs) and we explore various aspects of this idea. Supporting evidence includes global symmetries, the ability of twin quivers to encode the generalized -rule, and the connection between the mutations of polytopes and of configurations of webs of 5-branes suspended from 7-branes. We introduce three methods for constructing twin quivers for GTPs. We also investigate the connection between twin quivers obtained using different toric phases. Twin quivers provide a powerful new perspective on GTPs. The ideas presented in this paper may represent a step towards the generalization of brane tilings to GTPs.
arXiv comment51 pages, 42 figures. v2: typos corrected, references added
References in corpus (33)
- Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
- Five Dimensional SUSY Field Theories, Non-trivial Fixed Points and String Dynamics
- Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams
- Extremal Transitions and Five-Dimensional Supersymmetric Field Theories
- Gauge Theories from Toric Geometry and Brane Tilings
- Five-Dimensional Supersymmetric Gauge Theories and Degenerations of Calabi-Yau Spaces
- Branes, Superpotentials and Superconformal Fixed Points
- D-Brane Gauge Theories from Toric Singularities and Toric Duality
- Brane Dimers and Quiver Gauge Theories
- Branes and N=1 Duality in String Theory
- Webs of five-branes and N=2 superconformal field theories
- A Geometric Unification of Dualities
- Toric Duality as Seiberg Duality and Brane Diamonds
- Small Instantons, del Pezzo Surfaces and Type I' theory
- Toric Duality Is Seiberg Duality
- Phase Structure of D-brane Gauge Theories and Toric Duality
- Symmetries of Toric Duality
- The Master Space of N=1 Gauge Theories
- Quivers, Tilings, Branes and Rhombi
- D3-branes on partial resolutions of abelian quotient singularities of Calabi-Yau threefolds
- Bipartite Field Theories: from D-Brane Probes to Scattering Amplitudes
- A New Infinite Class of Quiver Gauge Theories
- Quiver theories, soliton spectra and Picard-Lefschetz transformations
- (5d RG-flow) Trees in the Tropical Rain Forest
- Mastering the Master Space
- (Symplectic) Leaves and (5d Higgs) Branches in the Poly(go)nesian Tropical Rain Forest
- Brane Tilings and Specular Duality
- Network and Seiberg Duality
- New Directions in Bipartite Field Theories
- Bipartite Field Theories from D-Branes
- The Geometry of On-Shell Diagrams
- Double Handled Brane Tilings
- Cluster Transformations from Bipartite Field Theories
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- Combinatorial and Algebraic Mutations of Toric Fano 3-folds and Mass Deformations of 2d (0,2) Quiver Gauge Theories
- Birational Transformations on Dimer Integrable Systems
- Birational Transformations and 2d (0,2) Quiver Gauge Theories beyond Toric Fano 3-folds
- Classification and Birational Equivalence of Dimer Integrable Systems for Reflexive Polygons
- Consistent Dimer Models on Surfaces with Boundary
- Quiver-Invariant Dualities between Brane Tilings