Remarks on quiver gauge theories from open topological string theory

Alexander Quintero Velez; Nils Carqueville

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Remarks on quiver gauge theories from open topological string theory

Nils Carqueville, Alexander Quintero Velez

High Energy Physics - Theory · Submitted 23 Dec 2009

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Then we show that it precisely reproduces the results of the method of brane tilings, without having to resort to any effective field theory computations.

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arXiv ID0912.4699 (version 4)

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CitationAlexander Quintero Velez, Nils Carqueville. "Remarks on quiver gauge theories from open topological string theory." arXiv:0912.4699 (2009). https://pith.science/paper/ODN7XMLV

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,162 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.95 · mentions code or data availability 0.02.

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We study effective quiver gauge theories arising from a stack of D3-branes on certain Calabi-Yau singularities. Our point of view is a first principle approach via open topological string theory. This means that we construct the natural A-infinity-structure of open string amplitudes in the associated D-brane category. Then we show that it precisely reproduces the results of the method of brane tilings, without having to resort to any effective field theory computations. In particular, we prove a general and simple formula for effective superpotentials.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study effective quiver gauge theories arising from a stack of D3-branes on certain Calabi-Yau singularities.	contribution 0.64	0.80	0.04	asserted 0.95
s1	Our point of view is a first principle approach via open topological string theory.	method 0.93	0.58	0.04	asserted 0.99
s2	This means that we construct the natural A-infinity-structure of open string amplitudes in the associated D-brane category.	method 0.97	0.82	0.06	asserted 0.97
s3	Then we show that it precisely reproduces the results of the method of brane tilings, without having to resort to any effective field theory computations.	result 0.99	0.94	0.58	asserted 1.00
s4	In particular, we prove a general and simple formula for effective superpotentials.	result 0.94	0.95	0.44	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 1.00.

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Original abstract

We study effective quiver gauge theories arising from a stack of D3-branes on certain Calabi-Yau singularities. Our point of view is a first principle approach via open topological string theory. This means that we construct the natural A-infinity-structure of open string amplitudes in the associated D-brane category. Then we show that it precisely reproduces the results of the method of brane tilings, without having to resort to any effective field theory computations. In particular, we prove a general and simple formula for effective superpotentials.

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5 arXiv papers cite this in 7 sentences

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Papers citing it · 6 sentences without a confident label

Cites it as background 1 paper

We also thank Alastair Craw for pointing out the reference [ref] , and Nils Carqueville and Alexander Quintero Velez for sending an earlier version of [ref] .

Exact Lefschetz fibrations associated with dimer models · Introduction · 0.81

What it cites · 30 sentences without a confident label

Uses the method or tool of 8 papers

To construct the $$-structure, we first use the elegant method of [ref] to find the higher products on $^b((Z))$ and then extend [ref] it to branes in $^b_Z((X))$.

A Geometric Unification of Dualities · Introduction and summary · 0.80
To construct the $$-structure, we first use the elegant method of [ref] to find the higher products on $^b((Z))$ and then extend [ref] it to branes in $^b_Z((X))$.

Sheaves on local Calabi-Yau varieties · Introduction and summary · 0.80
To construct the $$-structure, we first use the elegant method of [ref] to find the higher products on $^b((Z))$ and then extend [ref] it to branes in $^b_Z((X))$.

Suspending Lefschetz fibrations, with an application to Local Mirror Symmetry · Introduction and summary · 0.80

Compares with 3 papers

If we label the arrows as shown in [ref], then the brane tiling superpotential is [equation] where $ρ_1$, $ρ_2$ and $ρ_3$ are the deleted arrows corresponding to the perfect matching $π_10$; compare [ref] .

Toric Duality as Seiberg Duality and Brane Diamonds · An example: $dP_2$ · 0.80
If we label the arrows as shown in [ref], then the brane tiling superpotential is [equation] where $ρ_1$, $ρ_2$ and $ρ_3$ are the deleted arrows corresponding to the perfect matching $π_10$; compare [ref] .

Seiberg duality as derived equivalence for some quiver gauge theories · An example: $dP_2$ · 0.80
Finally, our proof differs from the one of [ref] in that we emphasise the role of the surface $Z$ and find the $$-structure on $^b_Z((X))$ by extending that of $^b((Z))$; to construct the latter we do not have to perform explicit calculations since we make use of Keller's higher multiplication theorem [ref] .

Exact Lefschetz fibrations associated with dimer models · Introduction and summary · 0.86

Cites as support 1 paper

A result of [ref] provides an equivalence between $^b_Z((X))$ and $^b_0(A)$.

T-structures on some local Calabi-Yau varieties · The $A_∞$-structure of the D-brane category $𝐃^b_Z(Coh(X))$ · 0.96

Cites as background 14 papers

In order to extract the data of the effective quiver gauge theory from the geometry of $Z$, several procedures have been developed in [ref] , most notably the fast inverse algorithm and the brane tiling method.

Properly ordered dimers, $R$-charges, and an efficient inverse algorithm · Introduction and summary · 0.85
In order to extract the data of the effective quiver gauge theory from the geometry of $Z$, several procedures have been developed in [ref] , most notably the fast inverse algorithm and the brane tiling method.

D-Brane Gauge Theories from Toric Singularities and Toric Duality · Introduction and summary · 0.85
In order to extract the data of the effective quiver gauge theory from the geometry of $Z$, several procedures have been developed in [ref] , most notably the fast inverse algorithm and the brane tiling method.

Phase Structure of D-brane Gauge Theories and Toric Duality · Introduction and summary · 0.85

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