Brane tilings

International Journal of Modern Physics A

Volumn 22, Issue 18, 2007, Pages 2977-3038

  Kennaway, Kristian D ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

AdS CFT; Brane tilings; Quiver gauge theories

Indexed keywords

EID: 34547557367     PISSN: 0217751X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217751X07036877     Document Type: Review

References (79)

1. O. Lunin and J. M. Maldacena, J. High Energy Phys. 05, 033 (2005), hep-th/0502086.
2. D. R. Morrison and M. R. Plesser, Adv. Theor. Math. Phys. 3, 1 (1999), hep-th/9810201.
3. J. P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Adv. Theor. Math. Phys. 8, 711 (2004), hep-th/0403002.
4. M. Cvetic, H. Lu, D. N. Page and C. N. Pope, Phys. Rev. Lett. 95, 071101 (2005), hep-th/0504225.
5. B. Feng, A. Hanany and Y.-H. He, Nucl. Phys. B 595, 165 (2001), hep-th/0003085.
6. Y.-H. He, Lectures on D-branes, gauge theories and Calabi-Yau singularities, hep-th/0408142.
7. M. R. Douglas, B. R. Greene and D. R. Morrison, Nucl. Phys. B 506, 84 (1997), hep-th/9704151.
8. A. Hanany and K. D. Kennaway, Dimer models and toric diagrams, hep-th/0503149.
9. S. Franco, A. Hanany, K. D. Kennaway, D. Vegh and B. Wecht, Brane dimers and quiver gauge theories, hep-th/0504110.
10. K. Intriligator and B. Wecht, Nucl. Phys. B 667, 183 (2003), hep-th/0304128.
11. I. R. Klebanov and E. Witten, Nucl. Phys. B 536, 199 (1998), hep-th/9807080.
12. M. R. Douglas and G. W. Moore, D-branes, quivers, and ALE instantons, hep-th/9603167.
13. Y. Imamura, H. Isono, K. Kimura and M. Yamazaki, Exactly marginal deformations of quiver gauge theories as seen from brane tilings, hep-th/0702049.
14. D. Forcella, A. Hanany and A. Zaffaroni, Baryonic generating functions, hep-th/0701236.
15. C. E. Beasley and M. R. Plesser, J. High Energy Phys. 12, 001 (2001), hep-th/0109053.
16. P. Kasteleyn, Graph theory and crystal physics, in Graph Theory and Theoretical Physics (Academic Press, London, 1967), pp. 43-110.
17. R. Kenyon, A. Okounkov and S. Sheffield, Dimers and amoebae, math-ph/0311005.
18. W. Fulton, Introduction to Toric Varieties (Princeton University Press, 1993).
19. O. Aharony, A. Hanany and B. Kol, J. High Energy Phys. 01, 002 (1998), hep-th/9710116.
20. Y. Imamura, J. High Energy Phys. 12, 041 (2006), hep-th/0609163.
21. S. Franco and D. Vegh, J. High Energy Phys. 11, 054 (2006), hep-th/0601063.
22. C. Beasley, B. R. Greene, C. I. Lazaroiu and M. R. Plesser, Nucl. Phys. B 566, 599 (2000), hep-th/9907186.
23. E. Witten, Nucl. Phys. B 403, 159 (1993), hep-th/9301042.
24. M. Buican, D. Malyshev, D. R. Morrison, M. Wijnholt and H. Verlinde, J. High Energy Phys. 01, 107 (2007), hep-th/0610007.
25. L. E. Ibanez, R. Rabadan and A. M. Uranga, Nucl. Phys. B 542, 112 (1999), hep-th/9808139.
26. K. Intriligator and N. Seiberg, J. High Energy Phys. 02, 031 (2006), hep-th/0512347.
27. A. Butti and A. Zaffaroni, R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization, hep-th/0506232.
28. X.-J. Wang and Y.-S. Wu, Nucl. Phys. B 683, 363 (2004), hep-th/0311073.
29. K. Kennaway, Work in progress.
30. A. Hanany, C. P. Herzog and D. Vegh, J. High Energy Phys. 07, 001 (2006), hep-th/0602041.
31. S. Benvenuti, B. Feng, A. Hanany and Y.-H. He, Counting BPS operators in gauge theories: Quivers, syzygies and plethystics, hep-th/0608050.
32. D. Martelli and J. Sparks, Nucl. Phys. B 759, 292 (2006), hep-th/0608060.
33. S. Franco et al., J. High Energy Phys. 01, 128 (2006), hep-th/0505211.
34. D. Martelli, J. Sparks and S. T. Yau, The geometric dual of a-maximisation for toric Sasaki-Einstein manifolds, hep-th/0503183.
35. R. Kenyon and A. Okounkov, Planar dimers and Harnack curves, math.ag/0311062.
36. K. Hori, A. Iqbal and C. Vafa, D-branes and mirror symmetry, hep-th/0005247.
37. K. Hori and C. Vafa, Mirror symmetry, hep-th/0002222.
38. A. Strominger, S.-T. Yau and E. Zaslow, Nucl. Phys. B 479, 243 (1996), hep-th/9606040.
39. M. Berkooz, M. R. Douglas and R. G. Leigh, Nucl. Phys. B 480, 265 (1996), hep-th/9606139.
40. B. Feng, Y.-H. He, K. D. Kennaway and C. Vafa, Dimer models from mirror symmetry and quivering amoebae, hep-th/0511287.
41. D. Bernstein, Funct. Anal. Appl. 9(2), 183 (1975).
42. A. G. Koushnirenko, Invent. Math. 32, 1 (1976).
43. A. Hanany and A. Iqbal, J. High Energy Phys. 04, 009 (2002), hep-th/0108137.
44. D. Auroux, L. Katzarkov and D. Orlov, Invent. Math. 166(3), 537 (2006), math/0506166.
45. S. Benvenuti and M. Kruczenski, J. High Energy Phys. 04, 033 (2006), hep-th/0505206.
46. S. Lins, Graphs of maps, Ph.D. thesis, math.CO/0305058.
47. C. Godsil and G. Royle, Algebraic Graph Theory, Graduate Texts in Mathematics, Vol. 207 (Springer, 2001).
48. D. Gabai, Duke Math. J. 53, 677 (1986).
49. G. Mikhalkin, Ann. Math. 2, 151 (2000), math/0010018.
50. G. Mikhalkin, Amoebas of algebraic varieties and tropical geometry, math.AG/0403015.
51. D. van Straten, Arctic computation of monodromy, in Komplexe Analysis, Oberwolfach 40/2006 (2006), pp. 41-43.
52. G. Pick, Sitzungber. Lotos 19, 311 (1899).
53. A. Hanany and A. Zaffaroni, J. High Energy Phys. 05, 001 (1998), hep-th/9801134.
54. M. Aganagic, A. Karch, D. Lust and A. Miemiec, Nucl Phys. B 569, 277 (2000), hep-th/9903093.
55. A. Hanany and A. M. Uranga, J. High Energy Phys. 05, 013 (1998), hep-th/9805139.
56. Y. Imamura, J. High Energy Phys. 06, 011 (2006), hep-th/0605097.
57. A. Hanany and D. Vegh, Quivers, tilings, branes and rhombi, hep-th/0511063.
58. A. Okounkov, N. Reshetikhin and C. Vafa, Quantum Calabi-Yau and classical crystals, hep-th/0309208.
59. J. Stienstra, Mahler measure variations, Eisenstein series and instanton expansions, math.NT/0502193.
60. J. J. Heckman and C. Vafa, Crystal melting and black holes, hep-th/0610005.
61. R. Dijkgraaf, D. Orlando and S. Reffert, Dimer models, free fermions and super quantum mechanics, arXiv:0705.1645.
62. S. Gukov and J. Walcher, Matrix factorizations and Kauffman homology, hep-th/0512298.
63. K. Kennaway and K. Hori, unpublished.
64. K. Ueda and M. Yamazaki, A note on brane tilings and McKay quivers, math.ag/0605780.
65. K. Ueda and M. Yamazaki, Brane tilings for parallelograms with application to homological mirror symmetry, math.ag/0606548.
66. K. Ueda and M. Yamazaki, Homological mirror symmetry for toric orbifolds of toric del Pezzo surfaces, math.ag/0703267.
67. S. Franco, A. Hanany, F. Saad and A. M. Uranga, J. High Energy Phys. 01, 011 (2006), hep-th/0505040.
68. A. Butti, D. Forcella and A. Zaffaroni, J. High Energy Phys. 09, 018 (2005), hep-th/0505220.
69. A. Brini and D. Forcella, J. High Energy Phys. 06, 050 (2006), hep-th/0603245.
70. I. Garcia-Etxebarria, F. Saad and A. M. Uranga, J. High Energy Phys. 06, 055 (2006), hep-th/0603108.
71. A. Butti, J. High Energy Phys. 10, 080 (2006), hep-th/0603253.
72. A. Butti, D. Forcella and A. Zaffaroni, J. High Energy Phys. 02, 081 (2007), hep-th/0607147.
73. I. Garcia-Etxebarria, F. Saad and A. M. Uranga, Supersymmetry breaking metastable vacua in runaway quiver gauge theories, arXiv:0704.0166.
74. I. Garcia-Etxebarria, F. Saad and A. M. Uranga, J. High Energy Phys. 08, 069 (2006), hep-th/0605166.
75. S. Lee, Phys. Rev. D 75, 101901 (2007), hep-th/0610204.
76. S. Lee, S. Lee and J. Park, Toric AdS(4)/CFT(3) duals and M-theory crystals, hep-th/0702120.
77. S. Kim, S. Lee, S. Lee and J. Park, Abelian gauge theory on M2-brane and toric duality, arXiv:0705.3540.
78. S. Benvenuti and M. Kruczenski, J. High Energy Phys. 10, 051 (2006), hep-th/0505046.
79. D. Sadri and M. M. Sheikh-Jabbari, J. High Energy Phys. 03, 024 (2006), hep-th/0510189.