Numerical Kähler-Einstein metric on the third del Pezzo

Communications in Mathematical Physics

Volumn 282, Issue 2, 2008, Pages 357-393

  Doran, Charles ^a   Headrick, Matthew ^b   Herzog, Christopher P ^c   Kantor, Joshua ^a   Wiseman, Toby ^d  

^a UNIVERSITY OF WASHINGTON   (United States)

^b STANFORD UNIVERSITY   (United States)

^c PRINCETON UNIVERSITY   (United States)

^d IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 47749085847     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-008-0558-6     Document Type: Article

References (42)

1. Yau, S.-T.: Calabi's Conjecture and some new results in algebraic geometry. Proc. Nat. Acad. Sci. 74, 1798 (1977)
2. Yau, S.-T.: On the Ricci curvature of a compact Kahler manifold and the complex Monge-Ampere equations. Comm. Pure App. Math. 31, 339-411 (1978)
3. Headrick, M., Wiseman, T.: Numerical Ricci-flat metrics on K3. Class. Quant. Grav. 22, 4931 (2005)
4. Donaldson, S.: Some numerical results in complex differential geometry. http://arXiv.org/list/math.DG/0512625, 2005
5. Douglas, M.R., Karp, R.L., Lukic, S., Reinbacher, R.: Numerical Calabi-Yau metrics. http://arXiv.org/list/hep-th/0612075, 2006
6. Douglas, M.R., Karp, R.L., Lukic, S., Reinbacher, R.: Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic. http://arXiv.org/ list/hep-th/0606261, 2006
7. 1(M) > 0. Invent. Math. 89, 225-246 (1987)
8. 1 > 0. Commun. Math. Phys. 112, 175-203 (1987)
9. Siu Y.T.: The existence of Kähler-Einstein metrics on manifolds with positive anticanonical line bundle and a suitable finite symmetry group. Ann. of Math. (2) 127(3), 585-627 (1988)
10. Feng, B., Hanany, A., He, Y.H.: Phase structure of D-brane gauge theories and toric duality. JHEP 0108, 040 (2001)
11. Hanany, A., Iqbal, A.: Quiver theories from D6-branes via mirror symmetry. JHEP 0204, 009 (2002)
12. Beasley, C.E., Plesser, M.R.: Toric duality is Seiberg duality. JHEP 0112, 001 (2001)
13. Klebanov I.R., Tseytlin A.A.: Gravity duals of supersymmetric SU(N) x SU(N+M) gauge theories. Nucl. Phys. B 578, 123 (2000)
14. Klebanov, I.R., Strassler, M.J.: Supergravity and a confining gauge theory: Duality cascades and chiSB-resolution of naked singularities. JHEP 0008, 052 (2000)
15. Abreu, M.: Kähler geometry of toric manifolds in symplectic coordinates. In: Symplectic and Contact Topology, Y. Eliashberg et al, eds. Fields Inst. Common., Providence, RI: Amer. Math. Soc., 2003, pp.1-24
16. Tian G., Zhu X.: Convergence of Kähler-Ricci Flow. J. Amer. Math. Soc. 20, 675-699 (2006)
17. Hori, K., Kapustin, A.: Duality of the fermionic 2d black hole and N = 2 Liouville theory as mirror symmetry, JHEP 0108, 045 (2001) http://arXiv.org/ list/hep-th/0104202, 2001
18. Garfinkle, D., Isenberg, J.: Critical behavior in Ricci flow, http://arXiv.org/list/arXiv:math.DG/0306129, 2003
19. Garfinkle, D., Isenberg, J.: Numerical studies of the behavior of Ricci flow. In: Geometric evolution equations, Vol. 367 of Contemp. Math., Providence, RI: Amer. Math. Soc., 2005, pp. 103-114
20. Headrick M., Wiseman T.: Ricci flow and black holes. Class. Quant. Grav. 23, 6683 (2006)
21. Headrick, M., Wiseman, T.: Numerical Kähler-Ricci soliton on the second del Pezzo. http://arXiv.org/abs/0706.2329, 2007
22. Wang X., Zhu X.: ä-Ricci solitons on toric manifolds with positive first Chern Class. Adv. Math. 188(1), 87-103 (2004)
23. Baytrev V., Selivanova E.: Einstein-ä metrics on symmetric toric Fano manifolds. J. Reine. Agnew. Math. 512, 225-236 (1999)
24. www.stanford.edu/~headrick/dP3/ www.phy.princeton.edu/~cpherzog/dP3/
25. Keller, J.: Ricci iterations on Kähler classes, http://arXiv.org/ abs/0709.1490, 2007
26. Giddings, S.B., Kachru, S., Polchinski, J.: "Hierarchies from fluxes in string compactifications," Phys. Rev. D 66, 106006 (2002)
27. Kachru S., Kallosh R., Linde A., Trivedi S.P.: De Sitter vacua in string theory. Phys. Rev. D 68, 046005 (2003)
28. Kachru, S., Kallosh, R., Linde, A., Maldacena, J.M., McAllister, L., Trivedi, S.P.: Towards inflation in string theory. JCAP 0310, 013 (2003)
29. Copeland, E.J., Myers, R.C., Polchinski, J.: Cosmic F- and D-strings. JHEP 0406, 013 (2004)
30. Altmann, K.: The versal deformation of an isolated toric Gorenstein singularity. http://arXiv.org/abs/alg-geom/9403004, 1994
31. Berenstein, D., Herzog, C.P., Ouyang, P., Pinansky, S.: Supersymmetry breaking from a Calabi-Yau singularity. JHEP 0509, 084 (2005)
32. Franco, S., Hanany, A., Saad, F., Uranga, A.M.: Fractional branes and dynamical supersymmetry breaking. JHEP 0601, 011 (2006)
33. Bertolini M., Bigazzi F., Cotrone A.L.: Supersymmetry breaking at the end of a cascade of Seiberg dualities. Phys. Rev. D 72, 061902 (2005)
34. Brini, A., Forcella, D.: Comments on the non-conformal gauge theories dual to Y(p,q) manifolds. JHEP 0606, 050 (2006)
35. Grana M., Polchinski J.: Supersymmetric three-form flux perturbations on AdS(5). Phys. Rev. D 63, 026001 (2001)
36. Matsushima Y.: Sur la structure du groupe d'homéomorphismes analytiques d'une certaine variété kaehlérienne. Nagoya Math. J. 11, 145-150 (1957)
37. Franco, S., He, Y.H., Herzog, C., Walcher, J.: Chaotic duality in string theory. Phys. Rev. D 70, 046006 (2004);
38. Franco, S., He, Y.H., Herzog, C., Walcher, J.: Chaotic cascades for D-branes on singularities. In: String theory: From Gange. Interactions to Cosuology (Cargese, 7-19 June 2004), NATO Science Servies II. Math. Phys. and Chem., Berlin-Heidelberge-New York: Springer 2006
39. Herzog, C.P., Ejaz, Q.J., Klebanov, I.R.: Cascading RG flows from new Sasaki-Einstein manifolds. JHEP 0502, 009 (2005)
40. Herzog C.P., Klebanov I.R.: On string tensions in supersymmetric SU(M) gauge theory. Phys. Lett. B 526, 388 (2002)
41. Guillemin V.: Kähler structures on toric varieties. J. Diff. Geom. 40, 285-309 (1994)
42. Fulton, W.: Introduction to Toric Varieties. Princeton NJ: Princeton University Press, 1993, p 92