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  • Open Access

Quiver-invariant dualities between brane tilings

Minsung Kho*

Seong-Jin Lee†

Rak-Kyeong Seong‡

  • *Contact author: minsung@unist.ac.kr
  • †Contact author: seongjinlee@ibs.re.kr
  • ‡Contact author: seong@unist.ac.kr
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Phys. Rev. D 113, 126007 – Published 5 June, 2026

DOI: https://doi.org/10.1103/j19n-t1ks

Abstract

We study pairs of 4d N=1 supersymmetric gauge theories that share the same vacuum moduli space and the same chiral field content, encoded by a common quiver, but differ in their superpotentials. These theories arise as worldvolume theories on a D3-brane probing a toric Calabi-Yau threefold and admit a description in terms of bipartite graphs on a 2-torus, known as brane tilings. Using an explicit example, we show that the correspondence is realized by a single “tilting” mutation along the diagonals of hexagonal faces in the brane tiling, which is equivalent to a specific sequence of Seiberg dualities performed at distinct gauge nodes in the quiver.

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References (60)

  1. S. Franco, A. Hanany, K. D. Kennaway, D. Vegh, and B. Wecht, Brane dimers and quiver gauge theories, J. High Energy Phys. 01 (2006) 096.
  2. A. Hanany and K. D. Kennaway, Dimer models and toric diagrams, arXiv:hep-th/0503149.
  3. S. Franco, A. Hanany, D. Martelli, J. Sparks, D. Vegh, and B. Wecht, Gauge theories from toric geometry and brane tilings, J. High Energy Phys. 01 (2006) 128.
  4. R. Kenyon, An introduction to the dimer model, arXiv:math/0310326.
  5. P. Kasteleyn, Graph theory and crystal physics, Graph Theory and Theoretical Physics (Academic Press, London, 1967), pp. 43–110.
  6. N. Seiberg, Electric—magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B435, 129 (1995).
  7. B. Feng, A. Hanany, and Y.-H. He, D-brane gauge theories from toric singularities and toric duality, Nucl. Phys. B595, 165 (2001).
  8. B. Feng, A. Hanany, Y.-H. He, and A. M. Uranga, Toric duality as Seiberg duality and brane diamonds, J. High Energy Phys. 12 (2001) 035.
  9. B. Feng, A. Hanany, and Y.-H. He, Phase structure of D-brane gauge theories and toric duality, J. High Energy Phys. 08 (2001) 040.
  10. B. Feng, S. Franco, A. Hanany, and Y.-H. He, Symmetries of toric duality, J. High Energy Phys. 12 (2002) 076.
  11. A. B. Goncharov and R. Kenyon, Dimers and cluster integrable systems, arXiv:1107.5588.
  12. M. Ciucu, A complementation theorem for perfect matchings of graphs having a cellular completion, J. Comb. Theory Ser. A 81, 34 (1998).
  13. R. W. Kenyon, J. G. Propp, and D. B. Wilson, Trees and matchings, arXiv:math/9903025.
  14. A. Butti, D. Forcella, A. Hanany, D. Vegh, and A. Zaffaroni, Counting chiral operators in quiver gauge theories, J. High Energy Phys. 11 (2007) 092.
  15. D. Forcella, A. Hanany, Y.-H. He, and A. Zaffaroni, The master space of N=1 gauge theories, J. High Energy Phys. 08 (2008) 012.
  16. D. Forcella, A. Hanany, Y.-H. He, and A. Zaffaroni, Mastering the master space, Lett. Math. Phys. 85, 163 (2008).
  17. M. Bianchi, S. Cremonesi, A. Hanany, J. F. Morales, D. Ricci Pacifici, and R.-K. Seong, Mass-deformed brane tilings, J. High Energy Phys. 10 (2014) 027.
  18. A. Higashitani and Y. Nakajima, Deformations of Dimer models, SIGMA 18, 030 (2022).
  19. S. Franco and R.-K. Seong, Twin theories, polytope mutations and quivers for GTPs, J. High Energy Phys. 07 (2023) 034.
  20. S. Cremonesi and J. Sá, Zig-zag deformations of toric quiver gauge theories. Part I. Reflexive polytopes, J. High Energy Phys. 05 (2024) 114.
  21. G. Arias-Tamargo, S. Franco, and D. Rodríguez-Gómez, The geometry of GTPs and 5d SCFTs, J. High Energy Phys. 07 (2024) 159.
  22. S. Franco and D. Rodriguez-Gomez, Quiver tails and brane webs, J. High Energy Phys. 10 (2024) 118.
  23. I. Carreño Bolla, S. Franco, and D. Rodríguez-Gómez, The 5d tangram: Brane webs, 7-branes and primitive T-cones, J. High Energy Phys. 05 (2025) 175.
  24. M. Kho, N. Lee, and R.-K. Seong, Birational transformations on dimer integrable systems, Phys. Rev. D 112, L041901 (2025).
  25. A. Hanany and R.-K. Seong, Brane tilings and specular duality, J. High Energy Phys. 08 (2012) 107.
  26. R. Kenyon, Local statistics of lattice dimers, Annales de L’Institut Henri Poincare Section (B) ProbabilityStatistics 33, 591 (1997).
  27. A. Amariti, M. Bianchi, M. Fazzi, S. Mancani, F. Riccioni, and S. Rota, Multi-planarizable quivers, orientifolds, and conformal dualities, J. High Energy Phys. 09 (2023) 094.
  28. W. Fulton, Introduction to Toric Varieties, No. 131 (Princeton University Press, Princeton, NJ, 1993).
  29. D. Cox, J. Little, and H. Schenck, Graduate Studies in Mathematics (American Mathematical Society, 2011)..
  30. E. Witten, Phases of N=2 theories in two-dimensions, Nucl. Phys. B403, 159 (1993).
  31. S. Benvenuti, B. Feng, A. Hanany, and Y.-H. He, Counting BPS operators in gauge theories: Quivers, syzygies and plethystics, J. High Energy Phys. 11 (2007) 050.
  32. A. Hanany and C. Romelsberger, Counting BPS operators in the chiral ring of N=2 supersymmetric gauge theories or N=2 braine surgery, Adv. Theor. Math. Phys. 11, 1091 (2007).
  33. B. Feng, A. Hanany, and Y.-H. He, Counting gauge invariants: The Plethystic program, J. High Energy Phys. 03 (2007) 090.
  34. K. A. Intriligator and B. Wecht, The exact superconformal R symmetry maximizes a, Nucl. Phys. B667, 183 (2003).
  35. A. Butti and A. Zaffaroni, R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization, J. High Energy Phys. 11 (2005) 019.
  36. A. Butti and A. Zaffaroni, From toric geometry to quiver gauge theory: The equivalence of a-maximization and Z-minimization, Fortschr. Phys. 54, 309 (2006).
  37. R. P. Stanley, Hilbert functions of graded algebras, Adv. Math. 28, 57 (1978).
  38. D. Martelli, J. Sparks, and S.-T. Yau, Sasaki-Einstein manifolds and volume minimisation, Commun. Math. Phys. 280, 611 (2008).
  39. D. Martelli, J. Sparks, and S.-T. Yau, The geometric dual of a-maximisation for Toric Sasaki-Einstein manifolds, Commun. Math. Phys. 268, 39 (2006).
  40. A. Butti, D. Forcella, and A. Zaffaroni, Counting BPS baryonic operators in CFTs with Sasaki-Einstein duals, J. High Energy Phys. 06 (2007) 069.
  41. J. Bao, E. Choi, Y.-H. He, R.-K. Seong, and S.-T. Yau, Futaki invariants and reflexive polygons, J. Math. Phys. (N.Y.) 66, 102302 (2025).
  42. A. Hanany and D. Vegh, Quivers, tilings, branes and rhombi, J. High Energy Phys. 10 (2007) 029.
  43. N. Broomhead, Dimer models and Calabi-Yau algebras, arXiv:0901.4662.
  44. C. Closset and M. Del Zotto, On 5D SCFTs and their BPS quivers. Part I: B-branes and brane tilings, Adv. Theor. Math. Phys. 26, 37 (2022).
  45. J. Davey, A. Hanany, and R.-K. Seong, Counting orbifolds, J. High Energy Phys. 06 (2010) 010.
  46. A. Hanany and R.-K. Seong, Symmetries of Abelian orbifolds, J. High Energy Phys. 01 (2011) 027.
  47. J. Davey, A. Hanany, and R.-K. Seong, An introduction to counting orbifolds, Fortschr. Phys. 59, 677 (2011).
  48. R. Eager, S. Franco, and K. Schaeffer, Dimer models and integrable systems, J. High Energy Phys. 06 (2012) 106.
  49. M. Kho, N. Lee, and R.-K. Seong, Classification and birational equivalence of dimer integrable systems for reflexive polygons, J. High Energy Phys. 02 (2026) 084.
  50. S. Franco, D. Ghim, S. Lee, R.-K. Seong, and D. Yokoyama, 2d (0,2) quiver gauge theories and D-branes, J. High Energy Phys. 09 (2015) 072.
  51. S. Franco, S. Lee, and R.-K. Seong, Brane brick models, toric Calabi-Yau 4-folds and 2d (0, 2) quivers, J. High Energy Phys. 02 (2016) 047.
  52. S. Franco, S. Lee, R.-K. Seong, and C. Vafa, Brane brick models in the mirror, J. High Energy Phys. 02 (2017) 106.
  53. S. Franco and R.-K. Seong, Fano 3-folds, reflexive polytopes and brane brick models, J. High Energy Phys. 08 (2022) 008.
  54. M. Kho and R.-K. Seong, On the master space for brane brick models, J. High Energy Phys. 09 (2023) 150.
  55. S. Franco, D. Ghim, G. P. Goulas, and R.-K. Seong, Mass deformations of brane brick models, J. High Energy Phys. 09 (2023) 176.
  56. M. Carcamo, S. Franco, D. Ghim, G. P. Goulas, and R.-K. Seong, Relevant deformations, brane brick models and triality, J. High Energy Phys. 04 (2026) 049.
  57. D. Ghim, M. Kho, and R.-K. Seong, Combinatorial and algebraic mutations of toric Fano 3-folds and mass deformations of 2d(0,2) quiver gauge theories, Phys. Rev. D 110, 086001 (2024).
  58. D. Ghim, M. Kho, and R.-K. Seong, Birational transformations and 2d (0, 2) quiver gauge theories beyond toric Fano 3-folds, J. High Energy Phys. 06 (2025) 032.
  59. D. Krefl, Brane tilings for orientifolds, Fortschr. Phys. 56, 869 (2008).
  60. A. Antinucci, S. Mancani, and F. Riccioni, Infrared duality in unoriented Pseudo del Pezzo, Phys. Lett. B 811, 135902 (2020).

Outline

Information

Phys. Rev. D 113, 126007– Published 5 June, 2026
  • Received 2 February 2026
  • Accepted 22 April 2026
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