Notes on toric Sasaki-Einstein seven-manifolds and AdS 4/CFT 3

Journal of High Energy Physics

Volumn 2008, Issue 11, 2008, Pages

  Martelli, Dario ^a   Sparks, James ^b  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

AdS CFT correspondence; Differential and algebraic geometry; Flux compactifications; Superstring vacua

Indexed keywords

EID: 84856403756     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2008/11/016     Document Type: Article

References (59)

1. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity 1998 Adv. Theor. Math. Phys. 2 231 [1999 Int. J. Theor. Phys. 38 1113 ] [hep-th/9711200]
2. J. Bagger and N. Lambert, Modeling multiple M2's 2007 Phys. Rev. D 75 045020 [hep-th/0611108]
3. A. Gustavsson, Algebraic structures on parallel M2-branes [0709.1260]
4. J. Bagger and N. Lambert, Gauge symmetry and supersymmetry of multiple M2-branes 2008 Phys. Rev. D 77 065008 [0711.0955]
5. J. Bagger and N. Lambert, Comments on multiple M2-branes 2008 J. High Energy Phys. JHEP02(2008)105 [0712.3738]
6. M. Van Raamsdonk, Comments on the Bagger-Lambert theory and multiple M2-branes 2008 J. High Energy Phys. JHEP05(2008)105 [0803.3803]
7. N. Lambert and D. Tong, Membranes on an orbifold 2008 Phys. Rev. Lett. 101 041602 [0804.1114]
8. J. Distler, S. Mukhi, C. Papageorgakis and M. Van Raamsdonk, M2-branes on M-folds 2008 J. High Energy Phys. JHEP05(2008)038 [0804.1256]
9. O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, [0806.1218]
10. A. Kehagias, New type IIB vacua and their F-theory interpretation 1998 Phys. Lett. B 435 337 [hep-th/9805131]
11. I.R. Klebanov and E. Witten, Superconformal field theory on threebranes at a Calabi-Yau singularity 1998 Nucl. Phys. B 536 199 [hep-th/9807080]
12. B.S. Acharya, J.M. Figueroa-O'Farrill, C.M. Hull and B.J. Spence, Branes at conical singularities and holography 1999 Adv. Theor. Math. Phys. 2 1249 [hep-th/9808014]
13. D.R. Morrison and M.R. Plesser, Non-spherical horizons. I 1999 Adv. Theor. Math. Phys. 3 1 [hep-th/9810201]
14. 5 solutions of M-theory 2004 Class. Quantum Grav. 21 4335 [hep-th/0402153]
15. 3 2004 Adv. Theor. Math. Phys. 8 711 [hep-th/0403002]
16. C.P. Boyer and K. Galicki, 3-Sasakian manifolds 1999 Surveys Diff. Geom. 7 123 [hep-th/9810250]
17. J.P. Gauntlett, D. Martelli, J.F. Sparks and D. Waldram, A new infinite class of Sasaki-Einstein manifolds 2006 Adv. Theor. Math. Phys. 8 987 [hep-th/0403038]
18. M.J. Duff, B.E.W. Nilsson and C.N. Pope, Kaluza-Klein supergravity 1986 Phys. Rep. 130 1
19. K. Oh and R. Tatar, Three dimensional SCFT from M2 branes at conifold singularities 1999 J. High Energy Phys. JHEP02(1999)025 [hep-th/9810244]
20. 3 2000 Nucl. Phys. B 577 547 [hep-th/9907219]
21. A. Ceresole, G. Dall'Agata, R. D'Auria and S. Ferrara, M-theory on the Stiefel manifold and 3D conformal field theories 2000 J. High Energy Phys. JHEP03(2000)011 [hep-th/9912107]
22. J.P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Supersymmetric AdS backgrounds in string and M-theory [hep-th/0411194]
23. W. Chen, H. Lü, C.N. Pope and J.F. Vazquez-Poritz, A note on Einstein-Sasaki metrics in D 7 2005 Class. Quantum Grav. 22 3421 [hep-th/0411218]
24. D. Martelli and J. Sparks, Toric geometry, Sasaki-Einstein manifolds and a new infinite class of AdS/CFT duals 2006 Comm. Math. Phys. 262 51 [hep-th/0411238]
25. E. Witten, Phases of = 2 theories in two dimensions, 1993 Nucl. Phys. B 403 159 [hep-th/9301042]
26. S. Benvenuti, S. Franco, A. Hanany, D. Martelli and J. Sparks, An infinite family of superconformal quiver gauge theories with Sasaki-Einstein duals 2005 J. High Energy Phys. JHEP06(2005)064 [hep-th/0411264]
27. M. Bertolini, F. Bigazzi and A.L. Cotrone, New checks and subtleties for AdS/CFT and a-maximization 2004 J. High Energy Phys. JHEP12(2004)024 [hep-th/0411249]
28. 3 correspondence 2008 J. High Energy Phys. JHEP09(2008)072 [0806.1519]
29. Y. Imamura and K. Kimura, Coulomb branch of generalized ABJM models [0806.3727]
30. S. Terashima and F. Yagi, Orbifolding the membrane action [0807.0368]
31. O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes [0807.4924]
32. D. Martelli and J. Sparks, Resolutions of non-regular Ricci-flat Kähler cones [0707.1674]
33. E. Lerman, Contact toric manifolds 2003 J. Symplectic Geom. 1 785 [math.SG/0107201]
34. E. Lerman, Homotopy groups of K-contact toric manifolds 2004 Trans. Am. Math. Soc. 356 4075 [math.SG/0204064]
35. R. Bott and L. Tu, Differential forms in algebraic topology Springer-Verlag, Germany (1982)
36. S.S. Gubser and I.R. Klebanov, Baryons and domain walls in an N = 1 superconformal gauge theory 1998 Phys. Rev. D 58 125025 [hep-th/9808075]
37. S. Franco et al., Gauge theories from toric geometry and brane tilings 2006 J. High Energy Phys. JHEP01(2006)128 [hep-th/0505211]
38. 4 duals 2005 J. High Energy Phys. JHEP08(2005)030 [hep-th/0505207]
39. D.P. Sorokin, V.I. Tkach and D.V. Volkov, On the relationship between compactified vacua of D = 11 and D = 10 supergravities 1985 Phys. Lett. B 161 301
40. B.E.W. Nilsson and C.N. Pope, Hopf fibration of eleven-dimensional supergravity 1984 Class. Quantum Grav. 1 499
41. M.R. Douglas and G.W. Moore, D-branes, quivers and ALE instantons [hep-th/9603167]
42. K.A. Intriligator and B. Wecht, The exact superconformal R-symmetry maximizes a 2003 Nucl. Phys. B 667 183 [hep-th/0304128]
43. D. Martelli, J. Sparks and S.-T. Yau, The geometric dual of a-maximisation for toric Sasaki-Einstein manifolds 2006 Comm. Math. Phys. 268 39 [hep-th/0503183]
44. D. Martelli, J. Sparks and S.-T. Yau, Sasaki-Einstein manifolds and volume minimisation 2008 Comm. Math. Phys. 280 611 [hep-th/0603021]
45. RR, 2005 Nucl. Phys. B 730 210 [hep-th/0507137]
46. I.R. Klebanov and A. Murugan, Gauge/gravity duality and warped resolved conifold 2007 J. High Energy Phys. JHEP03(2007)042 [hep-th/0701064]
47. I.R. Klebanov, A. Murugan, D. Rodriguez-Gomez and J. Ward, Goldstone bosons and global strings in a warped resolved conifold 2008 J. High Energy Phys. JHEP05(2008)090 [0712.2224]
48. D. Martelli and J. Sparks, Baryonic branches and resolutions of Ricci-flat Kähler cones 2008 J. High Energy Phys. JHEP04(2008)067 [0709.2894]
49. D. Martelli and J. Sparks, Symmetry-breaking vacua and baryon condensates in AdS/CFT [0804.3999]
50. J.P. Gauntlett, D. Martelli, J. Sparks and S.-T. Yau, Obstructions to the existence of Sasaki-Einstein metrics 2007 Comm. Math. Phys. 273 803 [hep-th/0607080]
51. D. Martelli and J. Sparks, Dual giant gravitons in Sasaki-Einstein backgrounds 2006 Nucl. Phys. B 759 292 [hep-th/0608060]
52. A. Butti, D. Forcella and A. Zaffaroni, Deformations of conformal theories and non-toric quiver gauge theories 2007 J. High Energy Phys. JHEP02(2007)081 [hep-th/0607147]
53. S. Benvenuti, B. Feng, A. Hanany and Y.-H. He, Counting BPS operators in gauge theories: quivers, syzygies and plethystics 2007 J. High Energy Phys. JHEP11(2007)050 [hep-th/0608050]
54. A. Hanany, N. Mekareeya and A. Zaffaroni, Partition functions for membrane theories 2008 J. High Energy Phys. JHEP09(2008)090 [0806.4212]
55. N.C. Leung and C. Vafa, Branes and toric geometry 1998 Adv. Theor. Math. Phys. 2 91 [hep-th/9711013]
56. S. Lee, Superconformal field theories from crystal lattices 2007 Phys. Rev. D 75 101901 [hep-th/0610204]
57. 3 duals and M-theory crystals 2007 J. High Energy Phys. JHEP05(2007)004 [hep-th/0702120]
58. S. Kim, S. Lee, S. Lee and J. Park, Abelian gauge theory on M2-brane and toric duality 2008 Nucl. Phys. B 797 340 [0705.3540]
59. 3 [0808.0912]