Quiver Theories from D6-branes via Mirror Symmetry

Amer Iqbal; Amihay Hanany

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Quiver Theories from D6-branes via Mirror Symmetry

Amihay Hanany, Amer Iqbal

High Energy Physics - Theory · Submitted 20 Aug 2001

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

The authors' main claim We argue that under local mirror symmetry D3-branes become D6-branes wrapped on a three torus in the mirror manifold.

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We study N=1 four dimensional quiver theories arising on the worldvolume of D3-branes at del Pezzo singularities of Calabi-Yau threefolds. We argue that under local mirror symmetry D3-branes become D6-branes wrapped on a three torus in the mirror manifold. The type IIB (p,q) 5-brane web description of the local del Pezzo, being closely related to the geometry of its mirror manifold, encodes the geometry of 3-cycles and is used to obtain gauge groups, quiver diagrams and the charges of the fractional branes.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study N=1 four dimensional quiver theories arising on the worldvolume of D3-branes at del Pezzo singularities of Calabi-Yau threefolds.	contribution 0.82	0.80	0.07	asserted 0.96
s1	We argue that under local mirror symmetry D3-branes become D6-branes wrapped on a three torus in the mirror manifold.	contribution 0.41	0.60	0.32	asserted 0.46
s2	The type IIB (p,q) 5-brane web description of the local del Pezzo, being closely related to the geometry of its mirror manifold, encodes the geometry of 3-cycles and is used to obtain gauge groups, quiver diagrams and the charges of the fractional branes.	method 0.96	0.76	0.25	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.83 · evidence from argument 0.85.

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The paper

Original abstract

We study N=1 four dimensional quiver theories arising on the worldvolume of D3-branes at del Pezzo singularities of Calabi-Yau threefolds. We argue that under local mirror symmetry D3-branes become D6-branes wrapped on a three torus in the mirror manifold. The type IIB (p,q) 5-brane web description of the local del Pezzo, being closely related to the geometry of its mirror manifold, encodes the geometry of 3-cycles and is used to obtain gauge groups, quiver diagrams and the charges of the fractional branes.

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References

Forward citations

Cited by 13 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Dimer models and toric diagrams
hep-th 2005-03 conditional novelty 8.0 of 10

The determinant of a dimer model's Kasteleyn matrix reproduces the linear sigma model field multiplicities of the corresponding toric diagram, giving a fast way to compute toric data and enumerate quiver phases.
An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals
hep-th 2004-11 accept novelty 8.0 of 10

An infinite family of quiver gauge theories is constructed and shown, via a-maximization, to reproduce exactly the central charges and baryon R-charges computed from the dual Sasaki-Einstein metrics.
Dimers and Orientifolds
hep-th 2007-07 accept novelty 7.0 of 10

A small set of rules on dimer diagrams determines the gauge theory on D3-branes at an orientifold of any toric Calabi-Yau singularity, recovering known orientifold models and generating new ones.
Gauge Theories at Resolved and Deformed Singularities using Dimers
hep-th 2006-03 conditional novelty 7.0 of 10

Dimer zig-zag path operations describe arbitrary partial resolutions and complex deformations of toric singularities, yielding the leftover D3-brane quiver gauge theories.
Dimer Models from Mirror Symmetry and Quivering Amoebae
hep-th 2005-11 conditional novelty 7.0 of 10

The dimer model encoding a toric quiver gauge theory is the intersection pattern of mirror D6-branes with a Riemann surface, projected onto a two-torus inside the D6-brane worldvolume.

Show 8 more citing papers

Quivers, Tilings, Branes and Rhombi
hep-th 2005-11 conditional novelty 7.0 of 10

A step-by-step algorithm constructs the brane tiling and quiver gauge theory directly from the toric diagram of a toric Calabi-Yau threefold, with R-charges read off as rhombus angles.
Gauge Theories from Toric Geometry and Brane Tilings
hep-th 2005-05 accept novelty 7.0 of 10

Toric data of a Calabi-Yau cone fixes the multiplicities, baryon and flavour charges and superpotential of the dual quiver gauge theory, and the theories for the L^{a,b,c} family are encoded by hexagonal brane tilings.
On 5d SCFTs and their BPS quivers. Part I: B-branes and brane tilings
hep-th 2019-12 conditional novelty 6.0 of 10

The BPS spectrum of a 5d SCFT on a circle is organized by the derived category of coherent sheaves on its Calabi-Yau singularity, realized concretely as a fractional-brane quiver for toric cases.
Chiral flavors and M2-branes at toric CY4 singularities
hep-th 2009-11 conditional novelty 6.0 of 10

Chirally flavored N=2 Chern-Simons quivers reproduce toric Calabi-Yau fourfolds with codimension-two singularities, via a conjectured quantum F-term relation between diagonal monopole operators and bifundamental fields.
Counting Chiral Operators in Quiver Gauge Theories
hep-th 2007-05 conditional novelty 6.0 of 10

The one-brane BPS generating function decomposes into GKZ geometric sectors carrying integer multiplicities, and the many-brane function follows by plethystic exponentiation of each sector.
Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
hep-th 2006-08 conditional novelty 6.0 of 10

The plethystic exponential of the single-trace BPS generating function gives the multi-trace generating function, and its inverse encodes the defining equations (syzygies) of the Calabi-Yau singularity.
Deformations of Toric Singularities and Fractional Branes
hep-th 2006-03 conditional novelty 6.0 of 10

Fractional deformation branes at toric singularities correspond to baryonic charges whose (p,q)-web weights are constant on Minkowski-sum subwebs, checked against examples and the deformed PdP4 geometry.
Brane Tilings
hep-th 2007-06 accept novelty 4.0 of 10

Toric quiver gauge theories are fully specified by bipartite tilings of a torus, and those tilings arise geometrically as the projection of mirror fractional D6-branes onto the mirror curve.

How the literature uses it

16 arXiv papers cite this in 30 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 17 sentences without a confident label

Uses its method or tool 2 papers

IIA Using SYZ-like mirror symmetry [ref] , one can arrive at the type IIA frame where D6 branes wrap a set of special Lagrangian 3-cycles $_i$ in the mirror CY 3-fold $X^∨$ [ref] .

Evidence for an algebra of $G_2$ instantons II · 7d/4d correspondence · 0.95
Then, the fractional brane charges can be obtained using the method described in [ref] : ch (F_1) = (-1, 0 ,0), ch(F_2) = (0, 1, 0), ch (F_3) = (1, -1, 1) , where the 3 entries are the D4-brane charge on $^1_1$, the D4-brane charge on $^1_2$, and the D2-brane charge respectively.

Higgsing M2-brane Theories · The $SPP$ theory with $k$ units of RR 2-form fluxes on both $^1$'s · 0.99

Uses its data or values 1 paper

Each of the 4 nodes in the quiver diagram (f:phase1f0) corresponds to a collection of fractional branes, whose charges are given respectively as (see (4.15) of [ref] ): ch(F_1) = (-1, 1,0, 0), ch(F_2) = (1, -1, 1, -1), ch(F_3) = (1, 0, -1, 0), ch(F_4) = (-1,0, 0,0) , Let us denote by $k_1$ and $k_2$ the RR 2-form fluxes on $^1_1$ and $^1_2$, and by $k_4$ the RR 4-form flux on $^1 ×^1$.

Higgsing M2-brane Theories · The $_0$ theory with $k$ units of RR 4-form flux on $^1 ×^1$ · 0.98

Compares with it 4 papers

After mutating with respect to nodes 5 and 8, in that order, and applying the cyclic permutation $(2, 6, 5, 4, 3, 7, 8)$ (or one of its images under the dihedral group $D_8$, which is a symmetry of the resulting quiver) one obtains the same quiver as in [ref] .

Vafa-Witten invariants from exceptional collections · $dP_5$ · 0.91
The result, shown in Figure [ref], coincides with descriptions found in the literature such as [ref] .

Exponential BPS graphs and D-brane counting on toric Calabi-Yau threefolds: Part II · Basic saddles and quiver · 0.99
The BPS quiver for the theory corresponding to local $dP_5$ is depicted in Figure [ref], and has adjacency matrix[This quiver is related by mutations to the one obtained in [ref] .

Quiver symmetries and wall-crossing invariance · dP5 · 0.95

Cites it as background 5 papers

The mirror configuration Under local mirror symmetry, a system of D3-branes located at the singular point of a non-compact toric Calabi-Yau 3-fold $$ are mapped to a set of D6-branes wrapping supersymmetric 3-cycles in the mirror Calabi-Yau $$ [ref] .

Dimers and Orientifolds · Review of the mirror picture · 0.98
The quivers $_$ are well-known [ref] .

On 5d SCFTs and their BPS quivers. Part I: B-branes and brane tilings · Rank-one examples: del Pezzo singularities · 0.80
The non toric case is still less understood: there exist studies on generalized conifolds [ref] , del Pezzo series [ref] , and more recently there was a proposal to construct new non toric examples [ref] .

Master Space and Hilbert Series for N=1 Field Theories · Toric Quiver Gauge Theories · 0.88

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