A geometric realization of confinement

Nuclear Physics B

Volumn 481, Issue 3, 1996, Pages 513-538

  Greene, Brian R ^a,d   Morrison, David R ^b   Vafa, Cumrun ^c  

^a Och Spine at New York Presbyterian Hospitals   (United States)

^b DUKE UNIVERSITY   (United States)

^c HARVARD UNIVERSITY   (United States)

^d Department of Obstetrics Gynecology   (United States)

Author keywords

Calabi Yau manifolds; Confinement; Nonperturbative effects in string theory; Type II string

Indexed keywords

EID: 0030590928     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(96)00465-8     Document Type: Article

References (44)

1. J. Polchinksi, Dirichlet Branes and Ramond-Ramond Charges, Phys. Rev. Lett. 75 (1995) 4724, hep-th/9510017.
2. E. Witten, String Theory Dynamics in Various Dimensions, Nucl. Phys. B 443 (1995) 85, hep-th/9503124.
3. A. Strominger, Massless Black Holes and Conifolds in String Theory, Nucl. Phys. B 451 (1995) 97, hep-th/9504090.
4. B.R. Greene, D.R. Morrison and A. Strominger, Black Hole Condensation and the Unification of String Vacua, Nucl. Phys. B 451 (1995) 109, hep-th/9504145.
5. C.H. Clemens, Double Solids, Adv. Math. 47 (1983) 107.
6. R. Friedman, Simultaneous Resolution of Threefold Double Points, Math. Ann. 274 (1986) 671.
7. F. Hirzebruch (notes by J. Werner), Some Examples of Threefolds with Trivial Canonical Bundle, in Gesammelte Abhandlungen, Band II (Springer, Berlin-New York, 1987) pp. 757-770.
8. 1 = 0 and x = -6, in Mathematical Aspects of String Theory, ed. S.-T. Yau (World Scientific, Singapore, 1987) pp. 629-646.
9. P. Candelas, A.M. Dale, C.A. Lütken and R. Schimmrigk, Complete Intersection Calabi-Yau Manifolds, Nucl. Phys. B 298 (1988) 493.
10. P.S. Green and T. Hübsch, Possible Phase Transitions Among Calabi-Yau Compactifications, Phys. Rev. Lett. 61 (1988) 1163; Connecting Moduli Spaces of Calabi-Yau Threefolds, Comm. Math. Phys. 119 (1988) 431.
11. P.S. Green and T. Hübsch, Possible Phase Transitions Among Calabi-Yau Compactifications, Phys. Rev. Lett. 61 (1988) 1163; Connecting Moduli Spaces of Calabi-Yau Threefolds, Comm. Math. Phys. 119 (1988) 431.
12. P. Candelas, P.S. Green and T. Hübsch, Finite Distance Between Distinct Calabi-Yau Manifolds, Phys. Rev. Lett. 62 (1989) 1956-1959; Rolling Among Calabi-Yau Vacua, Nucl. Phys. B 330 (1990) 49.
13. P. Candelas, P.S. Green and T. Hübsch, Finite Distance Between Distinct Calabi-Yau Manifolds, Phys. Rev. Lett. 62 (1989) 1956-1959; Rolling Among Calabi-Yau Vacua, Nucl. Phys. B 330 (1990) 49.
14. P. Candelas and X.C. de la Ossa, Comments on Conifolds, Nucl. Phys, B 342 (1990) 246.
15. K. Becker, M. Becker and A. Strominger, Fivebranes, Membranes and Non-Perturbative String Theory, Nucl. Phys. B 456 (1995) 130. hep-th/9507158.
16. R. Harvey and H.B. Lawson, Jr., Calibrated Geometries, Acta Math. 148 (1982) 47.
17. R.C. McLean, Deformations of Calibrated Submanifolds, J. Differential Geom., to appear, preprint at http://www.math.duke.edu/preprints/1996.html.
18. P.B. Kronheimer, The Construction of ALE Spaces as Hyper-Kähler Quotients, J. Differential Geom. 29 (1989) 665.
19. C. Vafa, Evidence for F-Theory, Nucl. Phys. B 469 (1996) 403, hep-th/9602022.
20. B.R. Greene, A. Shapere, C. Vafa and S.-T. Yau, Stringy Cosmic Strings, Nucl. Phys. B 337 (1990) 1.
21. N. Seiberg and A. Strominger, unpublished.
22. A. Hanany and I.R. Klebanov, On Tensionless Strings in 3 + 1 Dimensions, hep-th/9606136.
23. J. Dai, R. Leigh and J. Polchinski, New Connections Between String Theories, Mod. Phys. Lett. A 4 (1989) 2073.
24. E. Witten, Bound States of Strings and p-Branes, Nucl. Phys. B 460 (1996) 335, hep-th/9510135.
25. M. Bershadsky, V. Sadov and C. Vafa, D-Branes and Topological Field Theories, Nucl. Phys. B 463 (1996) 420, hep-th/9511222.
26. P.S. Aspinwall, B.R. Greene and D.R. Morrison, Calabi-Yau Moduli Space, Mirror Manifolds and Space-Time Topology Change in String Theory, Nucl. Phys. B 416 (1994) 414, hep-th/9309097.
27. E. Witten, Phases of N = 2 Theories In Two Dimensions, Nucl. Phys. B 403 (1993) 159, hep-th/9301042.
28. D.R. Morrison, Through the Looking Glass, Lecture at CIRM Conf., Trento (June, 1994), to appear.
29. P.S. Aspinwall, B.R. Greene and D.R. Morrison, Measuring Small Distances in N = 2 Sigma Models, Nucl. Phys. B 420 (1994) 184, hep-th/9311042.
30. V.V. Batyrev, Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties, J. Alg. Geom. 3 (1994) 493, alg-geom/9310003.
31. P.S. Aspinwall, B.R. Greene and D.R. Morrison, Multiple Mirror Manifolds and Topology Change in String Theory, Phys. Lett. B 303 (1993) 249, hep-th/9301043.
32. P.S. Aspinwall, B.R. Greene and D.R. Morrison, The Monomial-Divisor Mirror Map, Internat. Math. Res. Notices (1993) 319, alg-geom/9309007.
33. N. Berkovits and W. Siegel, Superspace Effective Actions for 4D Compactifications of Heterotic and Type II Superstrings, Nucl. Phys. B 462 (1996) 213, hep-th/9510106.
34. S. Cecotti, S. Ferrara and L. Girardello, Geometry of Type II Superstrings and the Moduli of Superconformal Field Theories, Int. J. Mod. Phys. A 4 (1989) 2475.
35. S. Ferrara and S. Sabharwal, Quaternionic Manifolds for Type II Superstring Vacua of Calabi-Yau Spaces, Nucl. Phys. B 332 (1990) 317.
36. N. Seiberg and E. Witten, Electric-Magnetic Duality, Monopole Condensation and Confinement in N = 2 Supersymmetric Yang-Mills Theory, Nucl. Phys. B 426 (1994) 19, hep-th/9407087.
37. S. Kachru and C. Vafa, Exact Results for N = 2 Compactifications of Heterotic Strings, Nucl. Phys. B 450 (1995) 69, hep-th/9505105.
38. S. Kachru, A. Klemm, W. Lerche, P. Mayr and C. Vafa, Non-Perturbative Results on the Point Particle Limit of N = 2 Heterotic String Compactifications, Nucl. Phys. B 459 (1996) 537, hep-th/9508155.
39. S. Lefschetz, L'Analysis Situs et la Géométrie Algébrique, Gauthier-Villars, Paris, 1924; reprinted in Selected Papers, Chelsea, New York, 1971, pp. 283-439.
40. N. Seiberg and E. Witten, Gauge Dynamics and Compactification to Three Dimensions, hep-th/9607163.
41. H. Ooguri and C. Vafa, Two-Dimensional Black Hole and Singularities of CY Manifolds, Nucl. Phys. B 463 (1996) 55, hep-th/9511164.
42. M. Bershadsky, V. Sadov and C. Vafa, D-Strings on D-Manifolds, Nucl. Phys. B 463 (1996) 398, hep-th/9510225.
43. A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. Warner, Self-Dual Strings and N = 2 Supersymmetric Field Theory, Nucl. Phys. B 477 (1996) 746, hep-th/9604034.
44. F. Quevedo and C.A. Trugenberger, Phases of Antisymmetric Tensor Field Theories, hep-th/9604196.