Stringy world branes and exponential hierarchies

Journal of High Energy Physics

Volumn 4, Issue 11, 2000, Pages 1-18

  Mayr, Peter ^a  

^a CERN   (Switzerland)

Author keywords

Extra Large Dimensions; M Theory; String Duality; Superstrings and Heterotic Strings

Indexed keywords

EID: 7044268158     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: 10.1088/1126-6708/2000/11/013     Document Type: Article

References (77)

1. E. Witten, Strong coupling expansion of Calabi-Yau compactification, Nucl. Phys. B 471 (1996) 135 [hep-th/9602070].
2. J.D. Lykken, Weak scale superstrings, Phys. Rev. D 54 (1996) 3693 [hep-th/9603133].
3. N. Arkani-Hamed, S. Dimopoulos and G. Dvali, The hierarchy problem and new dimensions at a millimeter, Phys. Lett. B 429 (1998) 263 [hep-ph/9803315]; I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos and G. Dvali, New dimensions at a millimeter to a fermi and superstrings at a TeV, Phys. Lett. B 436 (1998) 257 [hep-ph/9804398].
4. N. Arkani-Hamed, S. Dimopoulos and G. Dvali, The hierarchy problem and new dimensions at a millimeter, Phys. Lett. B 429 (1998) 263 [hep-ph/9803315]; I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos and G. Dvali, New dimensions at a millimeter to a fermi and superstrings at a TeV, Phys. Lett. B 436 (1998) 257 [hep-ph/9804398].
5. L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221]; An alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064].
6. L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221]; An alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064].
7. H. Verlinde, Holography and compactification, Nucl. Phys. B 580 (2000) 264 [hep-th/9906182].
8. C.S. Chan, P.L. Paul and H. Verlinde, A note on warped string compactification, Nucl. Phys. B 581 (2000) 156 [hep-th/0003236].
9. B.R. Greene, K. Schalm and G. Shiu, Warped compactifications in m and f theory, Nucl. Phys. B 584 (2000) 480 [hep-th/0004103].
10. K. Behrndt and M. Cvetič, Supersymmetric domain wall world from D = 5 simple gauged supergravity, Phys. Lett. B 475 (2000) 253 [hep-th/9909058].
11. A. Strominger, Superstrings with torsion, Nucl. Phys. B 274 (1986) 253.
12. B. de Wit, D.J. Smit and N.D. H. Dass, Residual supersymmetry of compactified D = 10 supergravity, Nucl. Phys. B 283 (1987) 165.
13. E. Witten, New issues in manifolds of SU(3) holonomy, Nucl. Phys. B 268 (1986) 79.
14. P. Hořava and E. Witten, Heterotic and type-I string dynamics from eleven dimensions, Nucl. Phys. B 460 (1996) 506 [hep-th/9510209]; Eleven-dimensional supergravity on a manifold with boundary, Nucl. Phys. B 475 (1996) 94 [hep-th/9603142].
15. P. Hořava and E. Witten, Heterotic and type-I string dynamics from eleven dimensions, Nucl. Phys. B 460 (1996) 506 [hep-th/9510209]; Eleven-dimensional supergravity on a manifold with boundary, Nucl. Phys. B 475 (1996) 94 [hep-th/9603142].
16. J. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200].
17. S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109]; E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150].
18. S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109]; E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150].
19. L. Susskind and E. Witten, The holographic bound in anti-de Sitter space, hep-th/9805114.
20. O. Aharony, M. Berkooz, D. Kutasov and N. Seiberg, Linear dilatons, NS five-branes and holography, J. High Energy Phys. 10 (1998) 004 [hep-th/9808149].
21. H. Verlinde, Supersymmetry at large distance scales, hep-th/0004003.
22. C. Schmidhuber, Micrometer gravitinos and the cosmological constant, Nucl. Phys. B 585 (2000) 385 [hep-th/0005248].
23. K. Benakli and Y. Oz, Small instantons and weak scale string theory, Phys. Lett. B 472 (2000) 83 [hep-th/9910090].
24. E. Witten, Small instantons in string theory, Nucl. Phys. B 460 (1996) 541 [hep-th/9511030].
25. M.J. Duff and J.X. Lu, Elementary five-brane solutions of D = 10 supergravity, Nucl. Phys. B 354 (1991) 141; A. Strominger, Heterotic solitons, Nucl. Phys. B 343 (1990) 167; C.G. Callan Jr., J.A. Harvey and A. Strominger, World sheet approach to heterotic instantons and solitons, Nucl. Phys. B 359 (1991) 611.
26. M.J. Duff and J.X. Lu, Elementary five-brane solutions of D = 10 supergravity, Nucl. Phys. B 354 (1991) 141; A. Strominger, Heterotic solitons, Nucl. Phys. B 343 (1990) 167; C.G. Callan Jr., J.A. Harvey and A. Strominger, World sheet approach to heterotic instantons and solitons, Nucl. Phys. B 359 (1991) 611.
27. M.J. Duff and J.X. Lu, Elementary five-brane solutions of D = 10 supergravity, Nucl. Phys. B 354 (1991) 141; A. Strominger, Heterotic solitons, Nucl. Phys. B 343 (1990) 167; C.G. Callan Jr., J.A. Harvey and A. Strominger, World sheet approach to heterotic instantons and solitons, Nucl. Phys. B 359 (1991) 611.
28. M. Green and J. Schwarz, Anomaly cancellation in supersymmetric D = 10 gauge theory and superstring theory, Phys. Lett. B 149 (1984) 117; M. Green and J. Schwarz, Infinity cancellations in SO(32) superstring theory, Phys. Lett. B 151 (1985) 21.
29. M. Green and J. Schwarz, Anomaly cancellation in supersymmetric D = 10 gauge theory and superstring theory, Phys. Lett. B 149 (1984) 117; M. Green and J. Schwarz, Infinity cancellations in SO(32) superstring theory, Phys. Lett. B 151 (1985) 21.
30. M.J. Duff, R. Minasian and E. Witten, Evidence for heterotic/heterotic duality, Nucl. Phys. B 465 (1996) 413 [hep-th/9601036].
31. V.A. Rubakov and M.E. Shaposhnikov, Extra space-time dimensions: towards a solution to the cosmological constant problem, Phys. Lett. B 125 (1993) 139.
32. 5 and the 4d cosmological constant, Nucl. Phys. B 580 (2000) 140 [hep-th/9912156].
33. 5 and the 4d cosmological constant, Nucl. Phys. B 580 (2000) 140 [hep-th/9912156].
34. P. Candelas, G.T. Horowitz, A. Strominger and E. Witten, Vacuum configurations for superstrings, Nucl. Phys. B 258 (1985) 46.
35. For a review and original references, see H.P. Nilles, Gaugino condensation and supersymmetry breakdown, Int. J. Mod. Phys. A 5 (1990) 4199.
36. P. Mayr, On supersymmetry breaking in string theory and its realization in brane worlds, Nucl. Phys. B 593 (2001) 99 [hep-th/0003198].
37. P. Berglund and P. Mayr, Heterotic string/F-theory duality from mirror symmetry, Adv. Theor. Math. Phys. 2 (1999) 1307 [hep-th/9811217]; G. Rajesh, Toric geometry and F-theory/heterotic duality in four dimensions, J. High Energy Phys. 12 (1998) 018; D.-E. Diaconescu and G. Rajesh, Geometrical aspects of fivebranes in heterotic/F-theory duality in four dimensions, J. High Energy Phys. 06 (1999) 002; R. Donagi, B.A. Ovrut and D. Waldram, Moduli spaces of fivebranes on elliptic CalabiYau threefolds, J. High Energy Phys. 11 (1999) 030; P. Berglund and P. Mayr, Stability of vector bundles from F-theory, J. High Energy Phys. 12 (1999) 009; A. Grassi, Z. Guralnik and B. Ovrut, Five-brane BPS states in heterotic M-theory, hep-th/0005121.
38. P. Berglund and P. Mayr, Heterotic string/F-theory duality from mirror symmetry, Adv. Theor. Math. Phys. 2 (1999) 1307 [hep-th/9811217]; G. Rajesh, Toric geometry and F-theory/heterotic duality in four dimensions, J. High Energy Phys. 12 (1998) 018; D.-E. Diaconescu and G. Rajesh, Geometrical aspects of fivebranes in heterotic/F-theory duality in four dimensions, J. High Energy Phys. 06 (1999) 002; R. Donagi, B.A. Ovrut and D. Waldram, Moduli spaces of fivebranes on elliptic CalabiYau threefolds, J. High Energy Phys. 11 (1999) 030; P. Berglund and P. Mayr, Stability of vector bundles from F-theory, J. High Energy Phys. 12 (1999) 009; A. Grassi, Z. Guralnik and B. Ovrut, Five-brane BPS states in heterotic M-theory, hep-th/0005121.
39. P. Berglund and P. Mayr, Heterotic string/F-theory duality from mirror symmetry, Adv. Theor. Math. Phys. 2 (1999) 1307 [hep-th/9811217]; G. Rajesh, Toric geometry and F-theory/heterotic duality in four dimensions, J. High Energy Phys. 12 (1998) 018; D.-E. Diaconescu and G. Rajesh, Geometrical aspects of fivebranes in heterotic/F-theory duality in four dimensions, J. High Energy Phys. 06 (1999) 002; R. Donagi, B.A. Ovrut and D. Waldram, Moduli spaces of fivebranes on elliptic CalabiYau threefolds, J. High Energy Phys. 11 (1999) 030; P. Berglund and P. Mayr, Stability of vector bundles from F-theory, J. High Energy Phys. 12 (1999) 009; A. Grassi, Z. Guralnik and B. Ovrut, Five-brane BPS states in heterotic M-theory, hep-th/0005121.
40. P. Berglund and P. Mayr, Heterotic string/F-theory duality from mirror symmetry, Adv. Theor. Math. Phys. 2 (1999) 1307 [hep-th/9811217]; G. Rajesh, Toric geometry and F-theory/heterotic duality in four dimensions, J. High Energy Phys. 12 (1998) 018; D.-E. Diaconescu and G. Rajesh, Geometrical aspects of fivebranes in heterotic/F-theory duality in four dimensions, J. High Energy Phys. 06 (1999) 002; R. Donagi, B.A. Ovrut and D. Waldram, Moduli spaces of fivebranes on elliptic CalabiYau threefolds, J. High Energy Phys. 11 (1999) 030; P. Berglund and P. Mayr, Stability of vector bundles from F-theory, J. High Energy Phys. 12 (1999) 009; A. Grassi, Z. Guralnik and B. Ovrut, Five-brane BPS states in heterotic M-theory, hep-th/0005121.
41. P. Berglund and P. Mayr, Heterotic string/F-theory duality from mirror symmetry, Adv. Theor. Math. Phys. 2 (1999) 1307 [hep-th/9811217]; G. Rajesh, Toric geometry and F-theory/heterotic duality in four dimensions, J. High Energy Phys. 12 (1998) 018; D.-E. Diaconescu and G. Rajesh, Geometrical aspects of fivebranes in heterotic/F-theory duality in four dimensions, J. High Energy Phys. 06 (1999) 002; R. Donagi, B.A. Ovrut and D. Waldram, Moduli spaces of fivebranes on elliptic CalabiYau threefolds, J. High Energy Phys. 11 (1999) 030; P. Berglund and P. Mayr, Stability of vector bundles from F-theory, J. High Energy Phys. 12 (1999) 009; A. Grassi, Z. Guralnik and B. Ovrut, Five-brane BPS states in heterotic M-theory, hep-th/0005121.
42. P. Berglund and P. Mayr, Heterotic string/F-theory duality from mirror symmetry, Adv. Theor. Math. Phys. 2 (1999) 1307 [hep-th/9811217]; G. Rajesh, Toric geometry and F-theory/heterotic duality in four dimensions, J. High Energy Phys. 12 (1998) 018; D.-E. Diaconescu and G. Rajesh, Geometrical aspects of fivebranes in heterotic/F-theory duality in four dimensions, J. High Energy Phys. 06 (1999) 002; R. Donagi, B.A. Ovrut and D. Waldram, Moduli spaces of fivebranes on elliptic CalabiYau threefolds, J. High Energy Phys. 11 (1999) 030; P. Berglund and P. Mayr, Stability of vector bundles from F-theory, J. High Energy Phys. 12 (1999) 009; A. Grassi, Z. Guralnik and B. Ovrut, Five-brane BPS states in heterotic M-theory, hep-th/0005121.
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. S. Kachru and C. Vafa, Exact results for N = 2 compactifications of heterotic strings, Nucl. Phys. B 450 (1995) 69 [hep-th/9505105]; S. Ferrara, J. A. Harvey, A. Strominger and C. Vafa, Second quantized mirror symmetry, Phys. Lett. B 361 (1995) 59 [hep-th/9505162].
45. S. Kachru and C. Vafa, Exact results for N = 2 compactifications of heterotic strings, Nucl. Phys. B 450 (1995) 69 [hep-th/9505105]; S. Ferrara, J. A. Harvey, A. Strominger and C. Vafa, Second quantized mirror symmetry, Phys. Lett. B 361 (1995) 59 [hep-th/9505162].
46. E. Witten, Some comments on string dynamics, hep-th/9507121; M. Bershadsky, C. Vafa and V. Sadov, D-strings on D-manifolds, Nucl. Phys. B 463 (1996) 398 [hep-th/9510225]; A. Klemm and P. Mayr, Strong coupling singularities and non-abelian gauge symmetries in n = 2 string theory, Nucl. Phys. B 469 (1996) 37 [hep-th/9601014]; S. Katz, D.R. Morrison and M.R. Plesser, Enhanced gauge symmetry in type-II string theory, Nucl. Phys. B 477 (1996) 105 [hep-th/9601108].
47. E. Witten, Some comments on string dynamics, hep-th/9507121; M. Bershadsky, C. Vafa and V. Sadov, D-strings on D-manifolds, Nucl. Phys. B 463 (1996) 398 [hep-th/9510225]; A. Klemm and P. Mayr, Strong coupling singularities and non-abelian gauge symmetries in n = 2 string theory, Nucl. Phys. B 469 (1996) 37 [hep-th/9601014]; S. Katz, D.R. Morrison and M.R. Plesser, Enhanced gauge symmetry in type-II string theory, Nucl. Phys. B 477 (1996) 105 [hep-th/9601108].
48. E. Witten, Some comments on string dynamics, hep-th/9507121; M. Bershadsky, C. Vafa and V. Sadov, D-strings on D-manifolds, Nucl. Phys. B 463 (1996) 398 [hep-th/9510225]; A. Klemm and P. Mayr, Strong coupling singularities and non-abelian gauge symmetries in n = 2 string theory, Nucl. Phys. B 469 (1996) 37 [hep-th/9601014]; S. Katz, D.R. Morrison and M.R. Plesser, Enhanced gauge symmetry in type-II string theory, Nucl. Phys. B 477 (1996) 105 [hep-th/9601108].
49. E. Witten, Some comments on string dynamics, hep-th/9507121; M. Bershadsky, C. Vafa and V. Sadov, D-strings on D-manifolds, Nucl. Phys. B 463 (1996) 398 [hep-th/9510225]; A. Klemm and P. Mayr, Strong coupling singularities and non-abelian gauge symmetries in n = 2 string theory, Nucl. Phys. B 469 (1996) 37 [hep-th/9601014]; S. Katz, D.R. Morrison and M.R. Plesser, Enhanced gauge symmetry in type-II string theory, Nucl. Phys. B 477 (1996) 105 [hep-th/9601108].
50. E. Witten, Heterotic string conformai field theory and ADE singularities, hep-th/9909229.
51. P. Mayr, Conformal field theories on K3 and three-dimensional gauge theories, J. High Energy Phys. 08 (2000) 042 [hep-th/9910268].
52. M. Rozali, Hypermultiplet moduli space and three dimensional gauge theories, J. High Energy Phys. 12 (1999) 013 [hep-th/9910238].
53. 4 couplings in M- and type-II theories on Calabi-Yau spaces, Nucl. Phys. B 507 (1997) 571 [hep-th/9707013].
54. S. Katz, A. Klemm and C. Vafa, Geometric engineering of quantum field theories, Nucl. Phys. B 497 (1997) 173 [hep-th/9609239]; S. Katz, P. Mayr and C. Vafa, Mirror symmetry and exact solution of 4d N = 2 gauge theories, 1, Adv. Theor. Math. Phys. 1 (1998) 53 [hep-th/9706110].
55. S. Katz, A. Klemm and C. Vafa, Geometric engineering of quantum field theories, Nucl. Phys. B 497 (1997) 173 [hep-th/9609239]; S. Katz, P. Mayr and C. Vafa, Mirror symmetry and exact solution of 4d N = 2 gauge theories, 1, Adv. Theor. Math. Phys. 1 (1998) 53 [hep-th/9706110].
56. Work in progress.
57. 8 instantons and tensionless non-critical strings, Nucl. Phys. B 474 (1996) 122 [hep-th/9602120]; N. Seiberg and E. Witten, Comments on string dynamics in six dimensions, Nucl. Phys. B 471 (1996) 121 [hep-th/9603003].
58. 8 instantons and tensionless non-critical strings, Nucl. Phys. B 474 (1996) 122 [hep-th/9602120]; N. Seiberg and E. Witten, Comments on string dynamics in six dimensions, Nucl. Phys. B 471 (1996) 121 [hep-th/9603003].
59. P. Ginsparg, Comment on toroidal compactification of heterotic superstrings, Phys. Rev. D 35 (1987) 648.
60. A. Strominger, Open p-branes, Phys. Lett. B 383 (1996) 44 [hep-th/9512059].
61. E. Witten, Five-branes and M-theory on an orbifold, Nucl. Phys. B 463 (1996) 383 [hep-th/9512219].
62. M.J. Duff, J.T. Liu and R. Minasian, Eleven-dimensional origin of string/string duality: a one-loop test, Nucl. Phys. B 452 (1995) 261 [hep-th/9506126].
63. 2, Phys. Rev. D 53 (1996) 6725 [hep-th/9602010].
64. 2, Phys. Rev. D 53 (1996) 6725 [hep-th/9602010].
65. R. Gueven, Black p-brane solutions of D = 11 supergravity theory, Phys. Lett. B 276 (1992) 49.
66. A. Lukas, B.A. Ovrut, K.S. Stelle and D. Waldram, The universe as a domain wall, Phys. Rev. D 59 (1999) 086001 [hep-th/9803235].
67. J. Polchinski and M.J. Strassler, The string dual of a confining four-dimensional gauge theory, hep-th/0003136; K. Pilch and N.P. Warner, N = 1 supersymmetric renormalization group flows from IIB supergravity, hep-th/0006066.
68. J. Polchinski and M.J. Strassler, The string dual of a confining four-dimensional gauge theory, hep-th/0003136; K. Pilch and N.P. Warner, N = 1 supersymmetric renormalization group flows from IIB supergravity, hep-th/0006066.
69. 2 heterotic string, Nucl. Phys. B 496 (1997) 149 [hep-th/9612108]; P.S. Aspinwall and D.R. Morrison, Point-like instantons on K3 orbifolds, Nucl. Phys. B 503 (1997) 533 [hep-th/9705104]; P. Berglund and P. Mayr, Heterotic string/F-theory duality from mirror symmetry, Adv. Theor. Math. Phys. 2 (1999) 1307 [hep-th/9811217]; P.S. Aspinwall, Aspects of the hypermultiplet moduli space in string duality, J. High Energy Phys. 04 (1998) 019 [hep-th/9802194]; P.S. Aspinwall and R.Y. Donagi, The heterotic string, the tangent bundle and derived categories, Adv. Theor. Math. Phys. 2 (1998) 1041 [hep-th/9806094].
70. 2 heterotic string, Nucl. Phys. B 496 (1997) 149 [hep-th/9612108]; P.S. Aspinwall and D.R. Morrison, Point-like instantons on K3 orbifolds, Nucl. Phys. B 503 (1997) 533 [hep-th/9705104]; P. Berglund and P. Mayr, Heterotic string/F-theory duality from mirror symmetry, Adv. Theor. Math. Phys. 2 (1999) 1307 [hep-th/9811217]; P.S. Aspinwall, Aspects of the hypermultiplet moduli space in string duality, J. High Energy Phys. 04 (1998) 019 [hep-th/9802194]; P.S. Aspinwall and R.Y. Donagi, The heterotic string, the tangent bundle and derived categories, Adv. Theor. Math. Phys. 2 (1998) 1041 [hep-th/9806094].
71. 2 heterotic string, Nucl. Phys. B 496 (1997) 149 [hep-th/9612108]; P.S. Aspinwall and D.R. Morrison, Point-like instantons on K3 orbifolds, Nucl. Phys. B 503 (1997) 533 [hep-th/9705104]; P. Berglund and P. Mayr, Heterotic string/F-theory duality from mirror symmetry, Adv. Theor. Math. Phys. 2 (1999) 1307 [hep-th/9811217]; P.S. Aspinwall, Aspects of the hypermultiplet moduli space in string duality, J. High Energy Phys. 04 (1998) 019 [hep-th/9802194]; P.S. Aspinwall and R.Y. Donagi, The heterotic string, the tangent bundle and derived categories, Adv. Theor. Math. Phys. 2 (1998) 1041 [hep-th/9806094].
72. 2 heterotic string, Nucl. Phys. B 496 (1997) 149 [hep-th/9612108]; P.S. Aspinwall and D.R. Morrison, Point-like instantons on K3 orbifolds, Nucl. Phys. B 503 (1997) 533 [hep-th/9705104]; P. Berglund and P. Mayr, Heterotic string/F-theory duality from mirror symmetry, Adv. Theor. Math. Phys. 2 (1999) 1307 [hep-th/9811217]; P.S. Aspinwall, Aspects of the hypermultiplet moduli space in string duality, J. High Energy Phys. 04 (1998) 019 [hep-th/9802194]; P.S. Aspinwall and R.Y. Donagi, The heterotic string, the tangent bundle and derived categories, Adv. Theor. Math. Phys. 2 (1998) 1041 [hep-th/9806094].
73. 2 heterotic string, Nucl. Phys. B 496 (1997) 149 [hep-th/9612108]; P.S. Aspinwall and D.R. Morrison, Point-like instantons on K3 orbifolds, Nucl. Phys. B 503 (1997) 533 [hep-th/9705104]; P. Berglund and P. Mayr, Heterotic string/F-theory duality from mirror symmetry, Adv. Theor. Math. Phys. 2 (1999) 1307 [hep-th/9811217]; P.S. Aspinwall, Aspects of the hypermultiplet moduli space in string duality, J. High Energy Phys. 04 (1998) 019 [hep-th/9802194]; P.S. Aspinwall and R.Y. Donagi, The heterotic string, the tangent bundle and derived categories, Adv. Theor. Math. Phys. 2 (1998) 1041 [hep-th/9806094].
74. 2 heterotic string, Nucl. Phys. B 496 (1997) 149 [hep-th/9612108]; P.S. Aspinwall and D.R. Morrison, Point-like instantons on K3 orbifolds, Nucl. Phys. B 503 (1997) 533 [hep-th/9705104]; P. Berglund and P. Mayr, Heterotic string/F-theory duality from mirror symmetry, Adv. Theor. Math. Phys. 2 (1999) 1307 [hep-th/9811217]; P.S. Aspinwall, Aspects of the hypermultiplet moduli space in string duality, J. High Energy Phys. 04 (1998) 019 [hep-th/9802194]; P.S. Aspinwall and R.Y. Donagi, The heterotic string, the tangent bundle and derived categories, Adv. Theor. Math. Phys. 2 (1998) 1041 [hep-th/9806094].
75. 2 heterotic string, Nucl. Phys. B 496 (1997) 149 [hep-th/9612108]; P.S. Aspinwall and D.R. Morrison, Point-like instantons on K3 orbifolds, Nucl. Phys. B 503 (1997) 533 [hep-th/9705104]; P. Berglund and P. Mayr, Heterotic string/F-theory duality from mirror symmetry, Adv. Theor. Math. Phys. 2 (1999) 1307 [hep-th/9811217]; P.S. Aspinwall, Aspects of the hypermultiplet moduli space in string duality, J. High Energy Phys. 04 (1998) 019 [hep-th/9802194]; P.S. Aspinwall and R.Y. Donagi, The heterotic string, the tangent bundle and derived categories, Adv. Theor. Math. Phys. 2 (1998) 1041 [hep-th/9806094].
76. M. Bershadsky, C. Vafa and V. Sadov, D-branes and topological field theories, Nucl. Phys. B 463 (1996) 420 [hep-th/9511222].
77. S. Kachru, N. Seiberg and E. Silverstein, SUSY gauge dynamics and singularities of 4d N = 1 string vacua, Nucl. Phys. B 480 (1996) 170 [hep-th/9605036].