Extremal transitions in heterotic string theory

Nuclear Physics B

Volumn 513, Issue 1-2, 1998, Pages 175-197

  Sharpe, Eric ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

Strings

Indexed keywords

EID: 0032473066     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(97)00710-4     Document Type: Article

References (66)

1. [1]M. Reid, The moduli space of 3-folds with K = 0 may nevertheless be irreducible, Math. Ann. 278 (1987) 329.
2. [2] P. Green and T. Hubsch, Possible phase transitions among Calabi-Yau compactifications, Phys. Rev. Lett. 61 (1988) 1163; P. Candelas, P. Greer and T. Hubsch, Rolling among Calabi-Yau vacua, Nucl. Phys. B 330 (1990) 49; P. Green and T. Hubsch, Connecting moduli spaces of Calabi-Yau threefolds, Comm. Math. Phys. 119 (1988) 431; P. Candelas, A. Dale, C. Lutken and R. Schimmrigk, Complete intersection Calabi-Yau manifolds, Nucl. Phys. B 298 (1988) 493.
3. [2] P. Green and T. Hubsch, Possible phase transitions among Calabi-Yau compactifications, Phys. Rev. Lett. 61 (1988) 1163; P. Candelas, P. Greer and T. Hubsch, Rolling among Calabi-Yau vacua, Nucl. Phys. B 330 (1990) 49; P. Green and T. Hubsch, Connecting moduli spaces of Calabi-Yau threefolds, Comm. Math. Phys. 119 (1988) 431; P. Candelas, A. Dale, C. Lutken and R. Schimmrigk, Complete intersection Calabi-Yau manifolds, Nucl. Phys. B 298 (1988) 493.
4. [2] P. Green and T. Hubsch, Possible phase transitions among Calabi-Yau compactifications, Phys. Rev. Lett. 61 (1988) 1163; P. Candelas, P. Greer and T. Hubsch, Rolling among Calabi-Yau vacua, Nucl. Phys. B 330 (1990) 49; P. Green and T. Hubsch, Connecting moduli spaces of Calabi-Yau threefolds, Comm. Math. Phys. 119 (1988) 431; P. Candelas, A. Dale, C. Lutken and R. Schimmrigk, Complete intersection Calabi-Yau manifolds, Nucl. Phys. B 298 (1988) 493.
5. [2] P. Green and T. Hubsch, Possible phase transitions among Calabi-Yau compactifications, Phys. Rev. Lett. 61 (1988) 1163; P. Candelas, P. Greer and T. Hubsch, Rolling among Calabi-Yau vacua, Nucl. Phys. B 330 (1990) 49; P. Green and T. Hubsch, Connecting moduli spaces of Calabi-Yau threefolds, Comm. Math. Phys. 119 (1988) 431; P. Candelas, A. Dale, C. Lutken and R. Schimmrigk, Complete intersection Calabi-Yau manifolds, Nucl. Phys. B 298 (1988) 493.
6. [3] A.C. Avram, M. Kreuzer, M. Mandelberg and H. Skarke, The web of Calabi-Yau hypersurfaces in toric varieties, hep-th/9703003; A.C. Avram, P. Candelas, D. Jancic, M. Mandelberg, On the connectedness of the moduli space of Calabi-Yau manifolds, hep-th/9511230, Nucl. Phys. B 465 (1996) 458.
7. [3] A.C. Avram, M. Kreuzer, M. Mandelberg and H. Skarke, The web of Calabi-Yau hypersurfaces in toric varieties, hep-th/9703003; A.C. Avram, P. Candelas, D. Jancic, M. Mandelberg, On the connectedness of the moduli space of Calabi-Yau manifolds, hep-th/9511230, Nucl. Phys. B 465 (1996) 458.
8. [3] A.C. Avram, M. Kreuzer, M. Mandelberg and H. Skarke, The web of Calabi-Yau hypersurfaces in toric varieties, hep-th/9703003; A.C. Avram, P. Candelas, D. Jancic, M. Mandelberg, On the connectedness of the moduli space of Calabi-Yau manifolds, hep-th/9511230, Nucl. Phys. B 465 (1996) 458.
9. [4] A. Strominger, Massless black holes and conifolds in string theory, hep-th/9504090, Nucl. Phys. B 451 (1995) 96.
10. [4] A. Strominger, Massless black holes and conifolds in string theory, hep-th/9504090, Nucl. Phys. B 451 (1995) 96.
11. [5] B. Greene, D. Morrison and A. Strominger, Black hole condensation and the unification of string vacua, hep-th/9504145, Nucl. Phys. B 451 (1995) 109.
12. [5] B. Greene, D. Morrison and A. Strominger, Black hole condensation and the unification of string vacua, hep-th/9504145, Nucl. Phys. B 451 (1995) 109.
13. [6] C. Vafa, Evidence for F theory, hep-th/9602022, Nucl. Phys. B 469 (1996) 403; D. Morrison and C. Vafa, Compactifications of F theory on Calabi-Yau threefolds I, II, hepth/9602114, Nucl. Phys. B 473 (1996) 74, hep-th/9603161, Nucl. Phys. B 476 (1996) 437.
14. [6] C. Vafa, Evidence for F theory, hep-th/9602022, Nucl. Phys. B 469 (1996) 403; D. Morrison and C. Vafa, Compactifications of F theory on Calabi-Yau threefolds I, II, hepth/9602114, Nucl. Phys. B 473 (1996) 74, hep-th/9603161, Nucl. Phys. B 476 (1996) 437.
15. [6] C. Vafa, Evidence for F theory, hep-th/9602022, Nucl. Phys. B 469 (1996) 403; D. Morrison and C. Vafa, Compactifications of F theory on Calabi-Yau threefolds I, II, hepth/9602114, Nucl. Phys. B 473 (1996) 74, hep-th/9603161, Nucl. Phys. B 476 (1996) 437.
16. [6] C. Vafa, Evidence for F theory, hep-th/9602022, Nucl. Phys. B 469 (1996) 403; D. Morrison and C. Vafa, Compactifications of F theory on Calabi-Yau threefolds I, II, hepth/9602114, Nucl. Phys. B 473 (1996) 74, hep-th/9603161, Nucl. Phys. B 476 (1996) 437.
17. [6] C. Vafa, Evidence for F theory, hep-th/9602022, Nucl. Phys. B 469 (1996) 403; D. Morrison and C. Vafa, Compactifications of F theory on Calabi-Yau threefolds I, II, hepth/9602114, Nucl. Phys. B 473 (1996) 74, hep-th/9603161, Nucl. Phys. B 476 (1996) 437.
18. [7] M. Bershadsky, K. Intriligator, S. Kachru, D. Morrison, V. Sadov and C. Vafa, Geometric singularities and enhanced gauge symmetries, hep-th/9605200.
19. [8] P. Aspinwall and M. Gross, The SO(32) heterotic string on a K3 surface, hep-th/9605131.
20. [9] M. Lynker and R. Schimmrigk, Conifold transitions and mirror symmetries, hep-th/9511058; I. Brunner, M. Lynker and R. Schimmrigk, Unification of M-and F-theory Calabi-Yau fourfold vacua, hep-th/9610195.
21. [9] M. Lynker and R. Schimmrigk, Conifold transitions and mirror symmetries, hep-th/9511058; I. Brunner, M. Lynker and R. Schimmrigk, Unification of M-and F-theory Calabi-Yau fourfold vacua, hep-th/9610195.
22. [10] A. Klemm, B. Lian, S-S. Roan and S-T. Yau, Calabi-Yau fourfolds for M-and F-theory compactifications, hep-th/9609239.
23. [11] R. Friedman, J. Morgan and E. Witten, Vector bundles and F theory, hep-th/9701162.
24. [12] S. Kachru and E. Silverstein, Chirality changing phase transitions in 4D string vacua, hep-th/9704185.
25. [13] M. Bershadsky, A. Johansen, T. Pantev and V. Sadov, On four-dimensional compactifications of F-theory, hep-th/9701165.
26. [14] R. Donagi, Principal bundles on elliptic fibrations, alg-geom/9702002.
27. [15] M. Bershadsky and V. Sadov, F theory on K3 × K3 and instantons on 7-branes, hep-th/9703194.
28. [16] B. Andreas, G. Curio and D. Lüst, N = 1 Dual string pairs and their massless spectra, hep-th/9703194.
29. [17] P. Aspinwall and D. Morrison, Point-like instantons on K3 orbifolds, hep-th/9705104.
30. [18] E. Sharpe, Extremal transitions and (0,2) models, to appear.
31. [19] J. Distler and S. Kachru, (0,2) Landau-Ginzburg theory, hep-th/9309110, Nucl. Phys. B 413 (1994) 213; J. Distler, Notes on (0,2) superconformal field theories, hep-th/9502012.
32. [19] J. Distler and S. Kachru, (0,2) Landau-Ginzburg theory, hep-th/9309110, Nucl. Phys. B 413 (1994) 213; J. Distler, Notes on (0,2) superconformal field theories, hep-th/9502012.
33. [19] J. Distler and S. Kachru, (0,2) Landau-Ginzburg theory, hep-th/9309110, Nucl. Phys. B 413 (1994) 213; J. Distler, Notes on (0,2) superconformal field theories, hep-th/9502012.
34. [20] S. Kachru, N. Seiberg and E. Silverstein, SUSY Gauge Dynamics and Singularities of 4D N = 1 String Vacua, hep-th/9605036, Nucl. Phys. B 480 (1996) 170.
35. [20] S. Kachru, N. Seiberg and E. Silverstein, SUSY Gauge Dynamics and Singularities of 4D N = 1 String Vacua, hep-th/9605036, Nucl. Phys. B 480 (1996) 170.
36. [21] C. Okonek, M. Schneider and H. Spindler, Vector bundles on complex projective spaces (Birkhauser, Boston, 1980).
37. [22] M. Duff, R. Minasian and E. Witten, Evidence for heterotic/heterotic duality, hep-th/9601036, Nucl. Phys. B 465 (1996) 413.
38. [22] M. Duff, R. Minasian and E. Witten, Evidence for heterotic /heterotic duality, hep-th/9601036, Nucl. Phys. B 465 (1996) 413.
39. [23] X.-G. Wen and E. Witten, World-sheet instantons and the Peccei-Quinn symmetry, Phys. Lett. B 166 (1986) 397; M. Dine, N. Seiberg, X.-G. Wen and E. Witten, Non-perturbative effects on the string world sheet I, II, Nucl. Phys. B 278 (1986) 769; 289 (1987) 319.
40. [23] X.-G. Wen and E. Witten, World-sheet instantons and the Peccei-Quinn symmetry, Phys. Lett. B 166 (1986) 397; M. Dine, N. Seiberg, X.-G. Wen and E. Witten, Non-perturbative effects on the string world sheet I, II, Nucl. Phys. B 278 (1986) 769; 289 (1987) 319.
41. [23] X.-G. Wen and E. Witten, World-sheet instantons and the Peccei-Quinn symmetry, Phys. Lett. B 166 (1986) 397; M. Dine, N. Seiberg, X.-G. Wen and E. Witten, Non-perturbative effects on the string world sheet I, II, Nucl. Phys. B 278 (1986) 769; 289 (1987) 319.
42. [24] E. Silverstein and E. Witten, Criteria for conformal invariance of (0,2) models, hep-th/9503212, Nucl. Phys. B 444 (1995) 161.
43. [24] E. Silverstein and E. Witten, Criteria for conformal invariance of (0,2) models, hep-th/9503212, Nucl. Phys. B 444 (1995) 161.
44. [25] E. Witten, Phases of N = 2 Theories in two dimensions, hep-th/9301042, Nucl. Phys. B 403 (1993) 159.
45. [25] E. Witten, Phases of N = 2 Theories in two dimensions, hep-th/9301042, Nucl. Phys. B 403 (1993) 159.
46. [26] A. Klemm, P. Mayr and C. Vafa, BPS states of exceptional non-critical strings, hep-th/9607139.
47. [27] R. Friedman and E Witten, private communication.
48. [28] D. Mumford, J. Fogarty and F. Kirwan, Geometric Invariant Theory (Springer, New York, 1994).
49. [29] R. Brussee, Stable bundles on blown up surfaces, Math. Z. 205 (1990) 551.
50. [30] E. Witten, Non-perturbative superpotentials in string theory, hep-th/9604030, Nucl. Phys. B 474 (1996) 343.
51. [30] E. Witten, Non-perturbative superpotentials in string theory, hep-th/9604030, Nucl. Phys. B 474 (1996) 343.
52. [31] R. Donagi, A. Grassi and E. Witten, A Non-perturbative superpotential with Eg-symmetry, hep-th/9607091.
53. [32] C. Vafa and E. Witten, A strong coupling test of S-duality, hep-th/9408074, Nucl. Phys. B 431 (1994) 3.
54. [32] C. Vafa and E. Witten, A strong coupling test of S-duality, hep-th/9408074, Nucl. Phys. B 431 (1994) 3.
55. [33] C. Vafa, Instantons on D-branes, hep-th/9512078, Nucl. Phys. B 463 (1996) 435.
56. [33] C. Vafa, Instantons on D-branes, hep-th/9512078, Nucl. Phys. B 463 (1996) 435.
57. [34] P. Griffiths and J. Harris Principles of Algebraic Geometry (Wiley, New York, 1978) p. 726.
58. [35] S.K. Donaldson and P.B. Kronheimer, The Geometry of Four-Manifolds (Oxford University Press, Oxford, 1990) Section 10.2.2.
59. [36] A. Beauville, Complex Algebraic Surfaces (Cambridge University Press, Cambridge, 1996).
60. [37] W. Fulton, Introduction to Toric Varieties (Princeton University Press, Princeton, 1993).
61. [38] T. Oda, Convex Bodies and Algebraic Geometry (Springer, New York, 1985).
62. [39] V.I. Danilov, The geometry of toric varieties, Russian Math Surveys 33:2 (1978) 97.
63. [40] D.A. Cox, The homogeneous coordinate ring of a toric variety, alg-geom/9210008.
64. [41] H. Matsumura, Commutative Ring Theory (Cambridge University Press, Cambridge, 1986).
65. [42] R. Hartshorne, Algebraic Geometry (Springer, New York, 1977).
66. [43] P.J. Hilton and U. Stammbach, A Course in Homological Algebra (Springer, New York, 1971).