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N. Seiberg, “Electric - magnetic duality in supersymmetric nonAbelian gauge theories,” Nucl. Phys. B 435
1995
Earlier work this paper cites.
S. Fomin and A. Zelevinsky, “Cluster algebras I. Foundations,” J. Amer. Math. Soc
Original
2002
Earlier work this paper cites.
J. Propp, “Generalized domino-shuffling,” Theoret. Comput. Sci. 303, no. 2-3, 267–301, Tilings of the plane (2003) [arXiv:math/0111034 [math.CO]]
2003
Earlier work this paper cites.
A. Butti, D. Forcella and A. Zaffaroni, “The Dual superconformal theory for L**pqr manifolds,” JHEP 0509
2005
Earlier work this paper cites.
S. Franco, A. Hanany, K. D. Kennaway, D. Vegh and B. Wecht, “Brane dimers and quiver gauge theories,” JHEP 0601
2006
Earlier work this paper cites.

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S. Franco, A. Hanany, D. Martelli, J. Sparks, D. Vegh and B. Wecht, “Gauge theories from toric geometry and brane tilings,” JHEP 0601
2006
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S. Fomin and A. Zelevinsky, “Cluster algebras IV: Coefficients,” Compos. Math. 143 (2007), 112–164
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2008
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2013

Franco, Sebastian

Bipartite field theories (BFTs) are a new class of 4d N=1 quantum field theories defined by bipartite graphs on bordered Riemann surfaces.

In this paper we derive, purely in terms of the gauge theory, the cluster transformations of face weights under square moves in the graph.
In this context, we obtain them by connecting regular parametrizations of the master space of the associated BFTs.
For BFTs on a disk, these transformations follow from the properties of coordinates in the Grassmannian.

N. Seiberg, “Electric - magnetic duality in supersymmetric nonAbelian gauge theories,” Nucl. Phys. B 435
1995
Earlier work this paper cites.
S. Fomin and A. Zelevinsky, “Cluster algebras I. Foundations,” J. Amer. Math. Soc
Original
2002
Earlier work this paper cites.
J. Propp, “Generalized domino-shuffling,” Theoret. Comput. Sci. 303, no. 2-3, 267–301, Tilings of the plane (2003) [arXiv:math/0111034 [math.CO]]
2003
Earlier work this paper cites.
A. Butti, D. Forcella and A. Zaffaroni, “The Dual superconformal theory for L**pqr manifolds,” JHEP 0509
2005
Earlier work this paper cites.
S. Franco, A. Hanany, K. D. Kennaway, D. Vegh and B. Wecht, “Brane dimers and quiver gauge theories,” JHEP 0601
2006
Earlier work this paper cites.

S. Franco, A. Hanany, D. Martelli, J. Sparks, D. Vegh and B. Wecht, “Gauge theories from toric geometry and brane tilings,” JHEP 0601
2006
Cited alongside, same era.
S. Franco and D. Vegh, “Moduli spaces of gauge theories from dimer models: Proof of the correspondence,” JHEP 0611
2006
Cited alongside, same era.
S. Fomin and A. Zelevinsky, “Cluster algebras IV: Coefficients,” Compos. Math. 143 (2007), 112–164
2007
Cited alongside, same era.
B. Feng, Y. -H. He, K. D. Kennaway and C. Vafa, “Dimer models from mirror symmetry and quivering amoebae,” Adv. Theor. Math. Phys. 12
2008
Cited alongside, same era.
D. Forcella, A. Hanany, Y. -H. He and A. Zaffaroni, “The Master Space of N=1 Gauge Theories,” JHEP 0808
Original
2008
Cited alongside, same era.