The geometric dual of a-maximisation for toric Sasaki-Einstein manifolds

Communications in Mathematical Physics

Volumn 268, Issue 1, 2006, Pages 39-65

  Martelli, Dario ^a   Sparks, James ^b,c   Yau, Shing Tung ^b  

^a CERN   (Switzerland)

^b HARVARD UNIVERSITY   (United States)

^c HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33749325672     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-006-0087-0     Document Type: Article

References (40)

1. 5 solutions of M-theory. Class. Quant. Grav. 21, 4335 (2004)
2. 3. Adv. Theor. Math. Phys. 8, 711 (2004)
3. Gauntlett, J.P., Martelli, D., Sparks, J., Waldram, D.: A new infinite class of Sasaki-Einstein manifolds. Adv. Theor. Math. Phys. 8, 987-1000 (2006)
4. Maldacena, J.M.: The large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2, 231 (1998)
5. [Int. J. Theor. Phys. 38, 1113 (1999).]
6. Kehagias, A.: New type IIB vacua and their F-theory interpretation. Phys. Lett. B 435, 337 (1998)
7. Klebanov, I.R., Wirten, E.: Superconformal field theory on threebranes at a Calabi-Yau singularity. Nucl. Phys. B 536, 199 (1998)
8. Acharya, B.S., Figueroa-O'Farrill, J.M., Hull, C.M., Spence, B.: Branes at conical singularities and holography. Adv. Theor. Math. Phys. 2, 1249 (1999)
9. Morrison, D.R., Plesser, M.R.: Non-spherical horizons. I. Adv. Theor. Math. Phys. 3, 1 (1999)
10. Martelli, D., Sparks, J.: Toric geometry, Sasaki-Einstein manifolds and a new infinite class of AdS/CFT duals. Commun. Math. Phys. 262, 51-89 (2006)
11. Benvenuti, S., Franco, S., Hanany, A., Martelli, D., Sparks, J.: An infinite family of superconformal quiver gauge theories with Sasaki-Einstein duals. JHEP 0506, 064 (2005)
12. Friedrich, Th., Kath, I.: Einstein manifolds of dimension five with small first eigenvalue of the Dirac operator. J. Differ. Geom. 29, 263-279 (1989)
13. 1(M) > 0. Invent. Math. 89, 225-246 (1987)
14. 1> 0. Commun. Math. Phys. 112, 175-203 (1987)
15. Boyer, C.P., Galicki, K.: New Einstein metrics in dimension five. J. Differ. Geom. 57(3), 443-463 (2001)
16. Gauntlett, J.P., Martelli, D., Sparks, J., Waldram, D.: Supersymmetric AdS Backgrounds in String and M-theory. To appear in the Proceedings of the 73rd Meeting between Physicists and Mathematicians "(A)dS/CFT correspondence", Strasbourg, September 11-13, 2003 de Gruyier, available at http://arXiv.org/list/hep-th/0411194, 2004
17. Chen, W., Lu, H., Pope, C.N., Vazquez-Poritz, J.F.: A note on Einstein-Sasaki metrics in D ≥ 7. Class. Quant. Grav. 22, 3421-3430 (2005)
18. Cheeger, J., Tian, G.: On the cone structure at infinity of Ricci flat manifolds with Euclidean volume growth and quadratic curvature decay. Invent. Math. 118(3), 493-571 (1994)
19. Feng, B., Hanany, A., He, Y.H.: D-brane gauge theories from toric singularities and toric duality. Nucl. Phys. B 595, 165 (2001)
20. Feng, B., Franco, S., Hanany, A., He, Y.H.: Symmetries of toric duality. JHEP 0212, 076 (2002)
21. Intriligator, K., Wecht, B.: The exact superconformal R-symmetry maximizes a. Nucl. Phys. B 667, 183 (2003)
22. Bertolini, M., Bigazzi, F., Cotrone, A.L.: New checks and subtleties for AdS/CFT and a-maximization. JHEP 0412, 024 (2004)
23. Besse, A.L.: Einstein Manifolds. Berlin-Heidelberg-New York: Springer-Verlag, 2nd edition, 1987
24. Guillemin, V.: Kähler Structures on Toric Varieties. J. Differ. Geom. 40, 285-309 (1994)
25. Abreu, M.: Kähler geometry of toric manifolds in symplectic coordinates. In: Batyrev, V. (ed.). To appear in Toric Varieties in Algebraic Geometry and Physics, AMS, available at http://arXiv.org/list/math.DG/0004122, 2000
26. Donaldson, S.K.: Scalar Curvature and Stability of Toric Varieties. J. Differ. Geom. 62, 289-349 (2002)
27. Donaldson, S.K.: Interior estimates for solutions of Abreu's equation. http://arXiv.org/list/ math.DG/0407486, 2004
28. Lerman, E.: Contact toric manifolds. J. Symplectic Geom. 1(4), 785-828 (2003)
29. Falcao de Moraes, S., Tomei, C.: Moment maps on symplectic cones. Pacific J. Math. 181(2), 357-375 (1997)
30. Delzant. T.: Hamiltoniens periodiques et images convexes de l'application moment. Bull. Soc. Math. France 116(3), 315-339 (1988)
31. Burns, D., Guillemin, V., Lerman, E.: Kaehler metrics on singular tone varieties, http://arXiv.oi-g/list/math.DG/0501311, 2005
32. Boyer, C.P., Galicki, K.: A Note on Toric Contact Geometry. J. Geom. Phys. 35(4), 288-298 (2000)
33. Lerman, E., Tolman, S.: Hamiltonian torus actions on symplectic orbifolds and toric varieties. Trans. Amer. Math. Soc. 349(10), 4201-4230 (1997)
34. Abreu, M.: Kähler geometry of toric varieties and extremal metrics. Int'l. J. Math. 9, 641-651 (1998)
35. Lasserre, J.B.: Integration and homogeneous functions. Proceedings of the American Mathematical Society 127, 813 (1999)
36. Herzog, C.P., Ejaz, Q.J., Klebanov, I.R.: Cascading RG flows from new Sasaki-Einstein manifolds. JHEP 0502, 009 (2005)
37. Cvetic, M., Lu, H., Page, D.N., Pope, C.N.: New Einstein-Sasaki Spaces in Five and Higher Dimensions. Phys. Rev. Lett. 95, 071101 (2005)
38. 3. Phys. Lett. B 621, 208-212 (2005)
39. Cvetic, M., Lu, H., Page, D.N., Pope, C.N.: New Einstein-Sasaki and Einstein Spaces from Kerr-de Sitter. http://arXiv.oi-g/list/hep-th/0505223.2005
40. Matsushima, Y.: Sur la structure du groupe d'homéomorphismes analytiques d'une certaine variété kaehlérienne. Nagoya Math. J. 11, 145-150 (1957)