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Probing the Space of Toric Quiver Theories
High Energy Physics - Theory · Submitted 15 Sep 2009
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We demonstrate a practical and efficient method for generating toric Calabi-Yau quiver theories, applicable to both D3 and M2 brane world-volume physics.
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The abstract, sentence by sentence
We demonstrate a practical and efficient method for generating toric Calabi-Yau quiver theories, applicable to both D3 and M2 brane world-volume physics. A new analytic method is presented at low order parametres and an algorithm for the general case is developed which has polynomial complexity in the number of edges in the quiver. Using this algorithm, carefully implemented, we classify the quiver diagram and assign possible superpotentials for various small values of the number of edges and nodes. We examine some preliminary statistics on this space of toric quiver theories.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We demonstrate a practical and efficient method for generating toric Calabi-Yau quiver theories, applicable to both D3 and M2 brane world-volume physics. | contribution 0.99 | 0.94 | 0.54 | asserted 1.00 |
| s1 | A new analytic method is presented at low order parametres and an algorithm for the general case is developed which has polynomial complexity in the number of edges in the quiver. | method 0.70 | 0.94 | 0.17 | asserted 1.00 |
| s2 | Using this algorithm, carefully implemented, we classify the quiver diagram and assign possible superpotentials for various small values of the number of edges and nodes. | contribution 0.42 | 0.96 | 0.13 | asserted 1.00 |
| s3 | We examine some preliminary statistics on this space of toric quiver theories. | result 0.61 | 0.90 | 0.08 | asserted 0.94 |
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The paper
Original abstract
We demonstrate a practical and efficient method for generating toric Calabi-Yau quiver theories, applicable to both D3 and M2 brane world-volume physics. A new analytic method is presented at low order parametres and an algorithm for the general case is developed which has polynomial complexity in the number of edges in the quiver. Using this algorithm, carefully implemented, we classify the quiver diagram and assign possible superpotentials for various small values of the number of edges and nodes. We examine some preliminary statistics on this space of toric quiver theories.
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References
How the literature uses it
11 arXiv papers cite this in 14 sentences
Papers citing it · 10 sentences without a confident label
Cites it as background 4 papers
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The study of $= 2$ quiver Chern-Simons theories dual to Calabi-Yau cones was initiated in [ref] , followed by a large number of works [ref] .
Chiral flavors and M2-branes at toric CY4 singularities · Introduction · 0.97
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Quivers are graphs that encode relevant pieces of information about the supersymmetric Lagrangian of a theory and, in the context of M2-branes in various backgrounds, they are believed to describe the $(2+1)$-dimensional CS theories that live on the M2-branes' world-volume [ref] .
M2-Branes and Fano 3-folds · Introduction · 0.85
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Extensive work has been done to study the moduli space of the supersymmetric gauge theories in 4 and 3 dimensions [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] .
M2-branes Theories without 3+1 Dimensional Parents via Un-Higgsing · $𝒩=2$ quiver Chern-Simons theories and Higgs branch · 1.00
What it cites · 16 sentences without a confident label
Builds on 1 paper
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First, we wish to continue with [ref] and exhaustively and progressively classify toric quiver diagrams with superpotential, whereby establishing, for each given number of nodes and edges, all possible parent $(3+1)$-dimensional theories which could descend to $(2+1)$-dimensional Chern-Simon quiver theories.
Chern-Simons: Fano and Calabi-Yau · Introduction · 0.98
Uses the method or tool of 2 papers
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One can be put these in by analysing candidates for the superpotentials as was done in [ref] .
M2-Branes and Quiver Chern-Simons: A Taxonomic Study · Quiver Diagrams for Low Order Parameters · 0.97
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The toric quiver theories have been produced specifically so the `forward algorithm' [ref] can be applied in order to scan through lower order theories, giving us a new method to study the duality manifested in the AdS/CFT correspondance.
D-Brane Gauge Theories from Toric Singularities and Toric Duality · Conclusions and Prospects · 0.99
Compares with 2 papers
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To further confirm the results the numbers of $x=2$ quiver diagrams are compared with the generating function found in [ref] , which gives the number of base quiver diagrams that have at least one non-vanishing toric superpotential.
M2-Branes and Quiver Chern-Simons: A Taxonomic Study · The Space of Quiver Theories · 0.99
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We would like to draw the reader's attention to a beautiful parallel work by [ref] , which also classifies toric quiver theories, but from the point of view of brane tilings.
On the Classification of Brane Tilings · Introduction · 0.97
Cites as background 24 papers
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Second, it is now well-established that toric Calabi-Yau brane theories admit a tiling or dimer description (see [ref] for excellent reviews); in order to admit a tiling, we must also adhere to a topological condition [equation]
Brane Tilings · Toric Calabi-Yau Quiver Gauge Theories · 0.84
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The works of [ref] have brought about tremendous interest in the M2-brane, and following [ref] , where the world-volume theory was realised as a Chern-Simons quiver theory in $(2+1)$-dimensions, much activity ensued (q.v. e.g. [ref] ).
Algebraic structures on parallel M2-branes · Introduction · 0.99
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The works of [ref] have brought about tremendous interest in the M2-brane, and following [ref] , where the world-volume theory was realised as a Chern-Simons quiver theory in $(2+1)$-dimensions, much activity ensued (q.v. e.g. [ref] ).
Membranes on an Orbifold · Introduction · 0.99
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