Remarks on quiver gauge theories from open topological string theory

Journal of High Energy Physics

Volumn 2010, Issue 3, 2010, Pages

  Carqueville, Nils ^a,b   Vélez, Alexander Quintero ^c  

^a UNIVERSITY OF MUNICH   (Germany)

^b EXCELLENCE CLUSTER UNIVERSE   (Germany)

^c UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

D branes; Supersymmetric effective theories; Topological strings

Indexed keywords

EID: 77954925955     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP03(2010)129     Document Type: Article

References (75)

1. M. Aganagic and C. Beem, The geometry of D-brane superpotentials, arXiv:0909.2245 [SPIRES].
2. M. Alim et al., Hints for off-shell mirror symmetry in type-II/F-theory compactifications, arXiv:0909.1842 [SPIRES].
3. M. Alim, M. Hecht, P. Mayr and A. Mertens, Mirror symmetry for toric branes on compact hypersurfaces, JHEP 09 (2009) 126 [arXiv:0901.2937] [SPIRES].
4. S.K. Ashok, E. Dell'Aquila, D.-E. Diaconescu and B. Florea, Obstructed D-branes in Landau-Ginzburg orbifolds, Adv. Theor. Math. Phys. 8 (2004) 427 [hep-th/0404167] [SPIRES].
5. P.S. Aspinwall, Topological D-branes and commutative algebra, hep-th/0703279 [SPIRES].
6. P.S. Aspinwall and L.M. Fidkowski, Superpotentials for quiver gauge theories, JHEP 10 (2006) 047 [hep-th/0506041] [SPIRES].
7. P.S. Aspinwall and A.E. Lawrence, Derived categories and zero-brane stability, JHEP 08 (2001) 004 [hep-th/0104147] [SPIRES].
8. M. R. Ballard, Sheaves on local Calabi-Yau varieties, arXiv:0801.3499.
9. M. Baumgartl, I. Brunner and M.R. Gaberdiel, D-brane superpotentials and RG flows on the quintic, JHEP 07 (2007) 061 [arXiv:0704.2666] [SPIRES].
10. M. Baumgartl and S. Wood, Moduli Webs and Superpotentials for Five-Branes, JHEP 06 (2009) 052 [arXiv:0812.3397] [SPIRES].
11. n and problems in linear algebra, Funktsional. Anal. I Prilozhen. 12 (1978) 68.
12. M. Bender and S. Mozgovoy, Crepant resolutions and brane tilings II: tilting bundles, arXiv:0909.2013.
13. A. Bondal and M. van den Bergh, Generators and representability of functors in commutative and noncommutative geometry, Mosc. Math. J. 3 (2003) 1 [math/0204218].
14. A.I. Bondal, Representations of associative algebras and coherent sheaves, Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989) 25.
15. T. Bridgeland, T-structures on some local Calabi-Yau varieties, math/0502050.
16. N. Broomhead, Dimer models and Calabi-Yau algebras, arXiv:0901.4662 [SPIRES].
17. I. Brunner, M.R. Douglas, A.E. Lawrence and C. Romelsberger, D-branes on the quintic, JHEP 08 (2000) 015 [hep-th/9906200] [SPIRES].
18. F. Cachazo, B. Fiol, K.A. Intriligator, S. Katz and C. Vafa, A geometric unification of dualities, Nucl. Phys. B 628 (2002) 3 [hep-th/0110028] [SPIRES].
19. N. Carqueville, Matrix factorisations and open topological string theory, JHEP 07 (2009) 005 [arXiv:0904.0862] [SPIRES].
20. K. Costello, Topological conformal field theories and Calabi-Yau categories, math/0412149.
21. A. Craw and G. G. Smith, Projective toric varieties as fine moduli spaces of quiver representations, Amer. J. Math. 130 (2008) 1509 [math/0608183].
22. M.R. Douglas, D-branes, categories and N = 1 supersymmetry, J. Math. Phys. 42 (2001) 2818 [hep-th/0011017] [SPIRES].
23. M.R. Douglas, S. Govindarajan, T. Jayaraman and A. Tomasiello, D-branes on Calabi-Yau manifolds and superpotentials, Commun. Math. Phys. 248 (2004) 85 [hep-th/0203173] [SPIRES].
24. M.R. Douglas and G.W. Moore, D-branes, quivers and ALE instantons, hep-th/9603167 [SPIRES].
25. B. Feng, A. Hanany and Y.-H. He, D-brane gauge theories from toric singularities and toric duality, Nucl. Phys. B 595 (2001) 165 [hep-th/0003085] [SPIRES].
26. B. Feng, A. Hanany and Y.-H. He, Phase structure of D-brane gauge theories and toric duality, JHEP 08 (2001) 040 [hep-th/0104259] [SPIRES].
27. B. Feng, A. Hanany, Y.-H. He and A.M. Uranga, Toric duality as Seiberg duality and brane diamonds, JHEP 12 (2001) 035 [hep-th/0109063] [SPIRES].
28. S. Franco, A. Hanany, K.D. Kennaway, D. Vegh and B. Wecht, Brane dimers and quiver gauge theories, JHEP 01 (2006) 096 [hep-th/0504110] [SPIRES].
29. S. Franco et al., Gauge theories from toric geometry and brane tilings, JHEP 01 (2006) 128 [hep-th/0505211] [SPIRES].
30. M. Futaki and K. Ueda, A-infinity categories associated with dimer models, arXiv:0912.1656.
31. S. Govindarajan and H. Jockers, Effective superpotentials for B-branes in Landau-Ginzburg models, JHEP 10 (2006) 060 [hep-th/0608027] [SPIRES].
32. T.W. Grimm, T.-W. Ha, A. Klemm and D. Klevers, The D5-brane effective action and superpotential in N = 1 compactifications, Nucl. Phys. B 816 (2009) 139 [arXiv:0811.2996] [SPIRES].
33. T.W. Grimm, T.-W. Ha, A. Klemm and D. Klevers, Computing brane and flux superpotentials in F-theory compactifications, arXiv:0909.2025 [SPIRES].
34. T.W. Grimm, T.-W. Ha, A. Klemm and D. Klevers, Five-brane superpotentials and heterotic/F-theory duality, arXiv:0912.3250 [SPIRES].
35. D.R. Gulotta, Properly ordered dimers, R-charges and an efficient inverse algorithm, JHEP 10 (2008) 014 [arXiv:0807.3012] [SPIRES].
36. A. Hanany, C.P. Herzog and D. Vegh, Brane tilings and exceptional collections, JHEP 07 (2006) 001 [hep-th/0602041] [SPIRES].
37. A. Hanany and K.D. Kennaway, Dimer models and toric diagrams, hep-th/0503149 [SPIRES].
38. M. Herbst, K. Hori and D. Page, Phases of N = 2 theories in 1 + 1 dimensions with boundary, arXiv:0803.2045 [SPIRES].
39. M. Herbst, C.-I. Lazaroiu and W. Lerche, Superpotentials, A∞ relations and WDVV equations for open topological strings, JHEP 02 (2005) 071 [hep-th/0402110] [SPIRES].
40. L. Hille and M. van den Bergh, Fourier-Mukai transforms, in Handbook of tilting theory, London Math. Soc. Lecture Note Ser. volume 332, Cambridge University Press, Cambridge U.K. (2007), page 147.
41. C. Hofman and W.-K. Ma, Deformations of topological open strings, JHEP 01 (2001) 035 [hep-th/0006120] [SPIRES].
42. A. Ishii and K. Ueda, Dimer models and exceptional collections, arXiv:0911.4529.
43. A. Ishii and K. Ueda, Dimer models and the special McKay correspondence, arXiv:0905.0059.
44. A. Ishii and K. Ueda, On moduli spaces of quiver representations associated with dimer models, RIMS Kõkyũroku Bessatsu B 9 (2008) 127 [arXiv:0710.1898].
45. H. Jockers and M. Soroush, Effective superpotentials for compact D5-brane Calabi-Yau geometries, Commun. Math. Phys. 290 (2009) 249 [arXiv:0808.0761] [SPIRES].
46. H. Jockers and M. Soroush, Relative periods and open-string integer invariants for a compact Calabi-Yau hypersurface, Nucl. Phys. B 821 (2009) 535 [arXiv:0904.4674] [SPIRES].
47. T. Kadeishvili, On the homology theory of fibre spaces (in Russian), Uspekhi Mat. Nauk 35 (1980) 183
48. [Math. Surveys 35 (1980) 231] [math.AT/0504437].
49. M.M. Kapranov, On the derived categories of coherent sheaves on some homogeneous spaces, Invent. Math. 92 (1988) 479.
50. B. Keller, A∞ algebras in representation theory, contribution to the proceedings of International Conference on Representations of A∞gebras and Related Topics (ICRA X), August 21-September 1, Beijing, China (2000).
51. B. Keller, Introduction to A∞ algebras and modules, Homol. Homotopy Appl. 3 (2001) 1 [math.RA/9910179].
52. B. Keller, A∞ algebras, modules and functor categories, Trends in representation theory of algebras and related topics, Contemp. Math. volume 406, American Mathematical Society, U.S.A. (2006).
53. A.D. King, Moduli of representations of finite-dimensional algebras, Quart. J. Math. Oxford Ser. 45 (1994) 515.
54. A. D. King, Tilting bundles on some rational surfaces, available at http://www.maths.bath.ac.uk/~masadk/papers/.
55. J. Knapp and E. Scheidegger, Towards open string mirror symmetry for one-parameter Calabi-Yau hypersurfaces, arXiv:0805.1013 [SPIRES].
56. M. Kontsevich, Formal (non)commutative symplectic geometry, in The Gelfand Mathematical Seminars, 1990-1992, Fields Institute Communications, Birkhäuser Boston U.S.A. (1993).
57. M. Kontsevich and Y. Soibelman, Homological mirror symmetry and torus fibrations, math/0011041.
58. C.I. Lazaroiu, Generating the superpotential on a D-brane category. I, hep-th/0610120 [SPIRES].
59. C.I. Lazaroiu, String field theory and brane superpotentials, JHEP 10 (2001) 018 [hep-th/0107162] [SPIRES].
60. C.I. Lazaroiu, On the non-commutative geometry of topological D-branes, JHEP 11 (2005) 032 [hep-th/0507222] [SPIRES].
61. K. Lefèvre-Hasegawa, Sur les A∞ catégories, math.CT/0310337.
62. ∞ structure on Ext-algebras, J. Pure Appl. Algebra 213 (2009) 2017 [math/0606144].
63. S.A. Merkulov, Strongly homotopy algebras of a Kähler manifold, Internat. Math. Res. Notices 3 (1999) 153 [math.AG/9809172].
64. D.R. Morrison and J. Walcher, D-branes and normal functions, arXiv:0709.4028 [SPIRES].
65. S. Mozgovoy, Crepant resolutions and brane tilings I: Toric realization, arXiv:0908.3475.
66. S. Mukhopadhyay and K. Ray, Seiberg duality as derived equivalence for some quiver gauge theories, JHEP 02 (2004) 070 [hep-th/0309191] [SPIRES].
67. A.N. Rudakov, Exceptional collections, mutations and helices, in Helices and vector bundles, London Math. Soc. Lecture Note Ser. volume 148, Cambridge University Press, Cambridge U.K. (1990), page 1.
68. ∞ deformation theory of a point and the derived categories of local Calabi-Yaus, J. Alg. 320 (2008) 3232 [math/0702539].
69. P. Seidel, Suspending Lefschetz fibrations, with an application to Local Mirror Symmetry, arXiv:0907.2063.
70. E.R. Sharpe, D-branes, derived categories and Grothendieck groups, Nucl. Phys. B 561 (1999) 433 [hep-th/9902116] [SPIRES].
71. J. Stienstra, Hypergeometric systems in two variables, quivers, dimers and dessins d'enfants, arXiv:0711.0464 [SPIRES].
72. A. Tomasiello, A-infinity structure and superpotentials, JHEP 09 (2001) 030 [hep-th/0107195] [SPIRES].
73. J. Walcher, Opening mirror symmetry on the quintic, Commun. Math. Phys. 276 (2007) 671 [hep-th/0605162] [SPIRES].
74. J. Walcher, Calculations for mirror symmetry with D-branes, JHEP 09 (2009) 129 [arXiv:0904.4905] [SPIRES].
75. E. Witten, Mirror manifolds and topological field theory, hep-th/9112056 [SPIRES].