On the structure of quadrilateral brane tilings

Paul de Medeiros

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On the structure of quadrilateral brane tilings

Paul de Medeiros

High Energy Physics - Theory · Submitted 26 May 2011

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

The authors' main claim We discuss the general structure of physically admissible quadrilateral brane tilings and Seiberg duality in terms of certain composite moves within this class.

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.26 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.08 · mentions code or data availability 0.02.

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Brane tilings provide the most general framework in string and M-theory for matching toric Calabi-Yau singularities probed by branes with superconformal fixed points of quiver gauge theories. The brane tiling data consists of a bipartite tiling of the torus which encodes both the classical superpotential and gauge-matter couplings for the quiver gauge theory. We consider the class of tilings which contain only tiles bounded by exactly four edges and present a method for generating any tiling within this class by iterating combinations of certain graph-theoretic moves. In the context of D3-branes in IIB string theory, we consider the effect of these generating moves within the corresponding class of supersymmetric quiver gauge theories in four dimensions. Of particular interest are their effect on the superpotential, the vacuum moduli space and the conditions necessary for the theory to reach a superconformal fixed point in the infrared. We discuss the general structure of physically admissible quadrilateral brane tilings and Seiberg duality in terms of certain composite moves within this class.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Brane tilings provide the most general framework in string and M-theory for matching toric Calabi-Yau singularities probed by branes with superconformal fixed points of quiver gauge theories.	background 1.00	0.05	0.04	asserted 1.00
s1	The brane tiling data consists of a bipartite tiling of the torus which encodes both the classical superpotential and gauge-matter couplings for the quiver gauge theory.	background 1.00	0.08	0.03	asserted 1.00
s2	We consider the class of tilings which contain only tiles bounded by exactly four edges and present a method for generating any tiling within this class by iterating combinations of certain graph-theoretic moves.	contribution 0.79	0.94	0.39	asserted 1.00
s3	In the context of D3-branes in IIB string theory, we consider the effect of these generating moves within the corresponding class of supersymmetric quiver gauge theories in four dimensions.	contribution 0.72	0.77	0.05	asserted 0.57
s4	Of particular interest are their effect on the superpotential, the vacuum moduli space and the conditions necessary for the theory to reach a superconformal fixed point in the infrared.	contribution 0.93	0.39	0.09	unclear 0.72
s5	We discuss the general structure of physically admissible quadrilateral brane tilings and Seiberg duality in terms of certain composite moves within this class.	contribution 0.99	0.87	0.34	asserted 0.88

What kind of paper the classifier reports this is: method or tool 0.88 · evidence from proof or derivation 0.95.

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Original abstract

Brane tilings provide the most general framework in string and M-theory for matching toric Calabi-Yau singularities probed by branes with superconformal fixed points of quiver gauge theories. The brane tiling data consists of a bipartite tiling of the torus which encodes both the classical superpotential and gauge-matter couplings for the quiver gauge theory. We consider the class of tilings which contain only tiles bounded by exactly four edges and present a method for generating any tiling within this class by iterating combinations of certain graph-theoretic moves. In the context of D3-branes in IIB string theory, we consider the effect of these generating moves within the corresponding class of supersymmetric quiver gauge theories in four dimensions. Of particular interest are their effect on the superpotential, the vacuum moduli space and the conditions necessary for the theory to reach a superconformal fixed point in the infrared. We discuss the general structure of physically admissible quadrilateral brane tilings and Seiberg duality in terms of certain composite moves within this class.

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Papers citing it

Cites it as background 1 paper

Graph-theoretic moves for generating classes of dimer models have recently investigated in [ref] .

Invariants of Toric Seiberg Duality · Concluding remarks and open questions · 0.99

What it cites · 83 sentences without a confident label

Uses the method or tool of 6 papers

Of course, as prescribed in [ref] , $Ψ_v$ also follows by applying the urban renewal' map to $v$ and then integrating out the massive fields associated with the two black bivalent vertices it produces.

Brane Dimers and Quiver Gauge Theories · Seiberg duality · 0.95
In such cases, the techniques developed in [ref] can be utilised to determine from the data for the toric Calabi-Yau singularity both the superpotential and the gauge-matter couplings in the dual field theory in terms of a quiver representation of the gauge group.

D-branes, Quivers, and ALE Instantons · Introduction · 0.98
In such cases, the techniques developed in [ref] can be utilised to determine from the data for the toric Calabi-Yau singularity both the superpotential and the gauge-matter couplings in the dual field theory in terms of a quiver representation of the gauge group.

Orbifold Resolution by D-Branes · Introduction · 0.98

Uses data or values from 1 paper

Amongst the smooth quadrilateral tilings in $$, the catalogue in [ref] lists one tiling with $t=2$ (catalogue #$(1.2)$), three tilings with $t=4$ (catalogue #$(2.4)-(2.6)$) and twelve tilings with $t=6$ (catalogue #$(3.26)-(3.37)$).

On the Classification of Brane Tilings · Examples · 1.00

Compares with 1 paper

The identification above has been observed already in [ref] and our composite move II corresponds a special case of their figure 13 (i.e. they are not working within the class of smooth quadrilateral tilings).

Brane Dimers and Quiver Gauge Theories · Smooth quadrilateral tilings · 0.92

Cites as support 7 papers

This inconsistency is shown in figure 15 of [ref] and is also implied by the results of [ref] .

Quivers, Tilings, Branes and Rhombi · Forbidden isolated faces · 0.99
This inconsistency is shown in figure 15 of [ref] and is also implied by the results of [ref] .

Quiver Topology and RG Dynamics · Forbidden isolated faces · 0.99
(However, it is worth mentioning that the effect of this duplication can be seen in the multiplicities of fields in the gauged linear sigma model description of $_τ_G⃗$ [ref] .) Despite seeming rather innocuous, notice that any such duplication must trigger an inconsistency in the associated superconformal field theory since [ref] implies $R_b + R_c =0$ for the new face bounded by $b$ and $c$.

Phase Structure of D-brane Gauge Theories and Toric Duality · Duplication and lagging · 0.96

Cites as background 42 papers

Seiberg duality for supersymmetric quiver gauge theories has been investigated in [ref] and identified with a certain geometric duality for toric Calabi-Yau manifolds in [ref] .

A Geometric Unification of Dualities · Introduction · 0.93
Seiberg duality for supersymmetric quiver gauge theories has been investigated in [ref] and identified with a certain geometric duality for toric Calabi-Yau manifolds in [ref] .

Brane Dimers and Quiver Gauge Theories · Introduction · 0.93
Seiberg duality for supersymmetric quiver gauge theories has been investigated in [ref] and identified with a certain geometric duality for toric Calabi-Yau manifolds in [ref] .

Duality Walls, Duality Trees and Fractional Branes · Introduction · 0.93

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