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Brane Tilings and Exceptional Collections
High Energy Physics - Theory · Submitted 5 Feb 2006
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We provide a dictionary that translates between these two heretofore unconnected languages.
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
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The abstract, sentence by sentence
Both brane tilings and exceptional collections are useful tools for describing the low energy gauge theory on a stack of D3-branes probing a Calabi-Yau singularity. We provide a dictionary that translates between these two heretofore unconnected languages. Given a brane tiling, we compute an exceptional collection of line bundles associated to the base of the non-compact Calabi-Yau threefold. Given an exceptional collection, we derive the periodic quiver of the gauge theory which is the graph theoretic dual of the brane tiling. Our results give new insight to the construction of quiver theories and their relation to geometry.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Both brane tilings and exceptional collections are useful tools for describing the low energy gauge theory on a stack of D3-branes probing a Calabi-Yau singularity. | background 1.00 | 0.05 | 0.05 | asserted 1.00 |
| s1 | We provide a dictionary that translates between these two heretofore unconnected languages. | contribution 0.98 | 0.94 | 0.35 | asserted 1.00 |
| s2 | Given a brane tiling, we compute an exceptional collection of line bundles associated to the base of the non-compact Calabi-Yau threefold. | method 0.52 | 0.95 | 0.17 | asserted 1.00 |
| s3 | Given an exceptional collection, we derive the periodic quiver of the gauge theory which is the graph theoretic dual of the brane tiling. | method 0.48 | 0.94 | 0.20 | asserted 1.00 |
| s4 | Our results give new insight to the construction of quiver theories and their relation to geometry. | interpretation 0.99 | 0.81 | 0.46 | asserted 0.98 |
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The paper
Original abstract
Both brane tilings and exceptional collections are useful tools for describing the low energy gauge theory on a stack of D3-branes probing a Calabi-Yau singularity. We provide a dictionary that translates between these two heretofore unconnected languages. Given a brane tiling, we compute an exceptional collection of line bundles associated to the base of the non-compact Calabi-Yau threefold. Given an exceptional collection, we derive the periodic quiver of the gauge theory which is the graph theoretic dual of the brane tiling. Our results give new insight to the construction of quiver theories and their relation to geometry.
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References
How the literature uses it
32 arXiv papers cite this in 60 sentences
Papers citing it · 43 sentences without a confident label
Uses its method or tool 5 papers
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Given a toric quiver $$ corresponding to a toric $CY_3$ $Y$, we can construct a tilting collection on any of the partial resolutions $Ỹ$ following [ref] .
Toric Fano varieties and Chern-Simons quivers · Tilting collection of line bundles from toric quiver · 0.81
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Given a dimer model of rank $r>0$, one can build a tilting collection of line bundles as follows [ref] .
On 5d SCFTs and their BPS quivers. Part I: B-branes and brane tilings · Tilting collections of line bundles · 0.93
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While the construction of exceptional collections is systemically possible using the techniques of [ref] , the resulting collections are generically incompatible with the standard “large volume” orientifold action.
The Standard Model Quiver in de Sitter String Compactifications · Conclusions · 0.91
Cites it as support 2 papers
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It follows from [ref] and [ref] that the condition $(4)$ of Lemma [ref] is satisfied if there exists an $R$-charge on the brane tiling.
On the noncommutative Donaldson-Thomas invariants arising from brane tilings · Path groupoid of a quiver potential · 0.97
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Mesons correspond to closed loops in the quiver and, as shown in [ref] , for any meson there is an F-term equivalent meson that passes for a given gauge group.
Master Space and Hilbert Series for N=1 Field Theories · The Mesonic Chiral Ring · 0.98
Cites it as background 6 papers
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In order to fully appreciate these statements we need to understand the structure of the mesonic chiral ring for toric theories [ref] .
On the geometry and the moduli space of beta-deformed quiver gauge theories · Non abelian BPS conditions · 0.94
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The resulting local Calabi-Yau's come with natural quivers that can be inferred from the toric data, which can be used either as the BPS quiver for $d=5$ Seiberg-Witten on a circle when one starts from M-theory on a circle times the Calabi-Yau [ref] , or for constructing (fractional) D3-probe field theories that explore the geometry [ref] .
Discrete Gauge Anomalies and Instantons · Are $SU(N)$ Theories with Anomaly Inflow Safe? · 0.85
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For a Calabi-Yau threefold the total space of the canonical line bundle over a Fano surface, nice bases of fractional branes can be found in terms of strongly exceptional collections [ref] .
B-branes and supersymmetric quivers in 2d · Fractional branes on a local $ℙ^3$ · 0.85
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