An Extended Lecture on Mirror Symmetry
S. Hosono; A. Klemm; S. Theisen
Recherche Coopérative sur Programme n°25 (1995)
- Volume: 47, page 33-76
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topHosono, S., Klemm, A., and Theisen, S.. "An Extended Lecture on Mirror Symmetry." Recherche Coopérative sur Programme n°25 47 (1995): 33-76. <http://eudml.org/doc/274892>.
@article{Hosono1995,
author = {Hosono, S., Klemm, A., Theisen, S.},
journal = {Recherche Coopérative sur Programme n°25},
language = {eng},
pages = {33-76},
publisher = {Institut de Recherche Mathématique Avancée - Université Louis Pasteur},
title = {An Extended Lecture on Mirror Symmetry},
url = {http://eudml.org/doc/274892},
volume = {47},
year = {1995},
}
TY - JOUR
AU - Hosono, S.
AU - Klemm, A.
AU - Theisen, S.
TI - An Extended Lecture on Mirror Symmetry
JO - Recherche Coopérative sur Programme n°25
PY - 1995
PB - Institut de Recherche Mathématique Avancée - Université Louis Pasteur
VL - 47
SP - 33
EP - 76
LA - eng
UR - http://eudml.org/doc/274892
ER -
References
top- [1] For introductions, see e.g. M. Green, J. Schwarz and E. Witten, Superstring Theory, Vols. I and II, Cambridge University Press, 1986; Zbl0619.53002
- D. Lust and S. Theisen, Lectures on String Theory, SpringerLecture Notes in Physics, Vol. 346, 1990; Zbl0716.53063MR1028064
- M. Kaku, Introduction to Superstrings, Springer1988 Zbl0655.58001MR954610
- [2] E. Verlinde, H. Verlinde, Lectures on String Perturbation Theory, in Superstrings88, Trieste Spring School, Ed. Greene et al. World Scientific (1989) 189 Zbl0985.81681MR1091556
- [3] C. Callan, D. Friedan, E. Martinec and M. Perry, Nucl. Phys. B262 (1985) 593, A. Sen, Phys. Rev. D32 (1985) 2102 and Phys. Rev. Lett.55 (1985) 1846 MR819433
- [4] D. Nemeschanski and A. Sen, Phys. Lett.178B (1986) 365
- [5] For review, see A. Giveon, M. Porrati and E. Rabinovici, Target Space Duality in String Theory, hep-th 9401139, to be published in Phys. Rep. MR1288936
- [6] L. Dixon in Proc. of the 1987 ICTP Summer Workshop in High Energy Physics and Cosmology, Trieste, ed. G. Furlan et al., World Scientific MR1026264
- [7] W. Lerche, C. Vafa and N. Warner, Nucl. Phys. B324 (1989) 427 MR1025424
- [8] B. Greene and M. Plesser, Nucl. Phys. B338 (1990) 15 MR1059831
- [9] Essays on Mirror Manifolds (ed. S.-T. Yau), Int. Press, Hong Kong, 1992
- [10] R. Dijkgraaf, E. Verlinde and H. Verlinde, Utrecht preprint THU-87/30; MR1002959
- A. Shapere and F. WilczekNucl. Phys. B320 (1989) 669; MR1004372
- A. Giveon, E. Rabinovici, G. Veneziano, Nucl. Phys. B322 (1989) 169
- [11] S. Ferrara and S. Theisen, Moduli Spaces, Effective Actions and Duality Symmetry in String Compactifications, in Proc. of the Third Hellenic School on Elementary Particle Physics, Corfu 1989, Argyres et al.(eds), World Scientific1990
- [12] P. Candelas, X. De la Ossa, P. Green and L. Parkes, Nucl. Phys. B359 (1991) 21
- [13] D. Morrison, Picard-Fuchs Equations and Mirror Maps for Hypersurfaces, in Essays on Mirror Manifolds (ed. S.-T. Yau), Int. Press, Hong Kong, 1992; Zbl0904.32020MR1191426
- A. Klemm and S. Theisen, Nucl. Phys. B389 (1993) 153; MR1202211
- A. Font, Nucl. Phys. B391 (1993) 358 MR1208020
- [14] A. Libgober and J. Teitelbaum, Duke Math. Journ., Int. Res. Notices1 (1993) 29; Zbl0789.14005MR1201748
- A. Klemm and S. Theisen, Mirror Maps and Instanton Sums for Complete Intersections in Weighted Projective Space, preprint LMU-TPW 93-08 Zbl1020.32507MR1287096
- [15] P. Candelas, X. de la Ossa, A. Font, S. Katz and D. Morrison, Mirror Symmetry for Two Parameter Models I, preprint CERN-TH.6884/93 Zbl0899.14017
- [16] S. Hosono, A. Klemm, S. Theisen and S.-T. Yau, Mirror Symmetry, Mirror Map and Applications to Calabi-Yau Hypersurfaces, to appear in Comm. Math. Phys. Zbl0814.53056MR1316509
- [17] S. Hosono, A. Klemm, S. Theisen and S.-T. Yau, Mirror Symmetry, Mirror Map and Applications to Complete Intersection Calabi-Yau Spaces, preprint LMU-TPW-94-03 (to appear) Zbl1020.32508MR1319280
- [18] P. Aspinwall. B. Greene and D. Morrison, Space-Time Topology Change: the Physicsof Calabi-Yau Moduli Space, preprint IASSNS-HEP-93-81; Zbl0844.32016
- P. Aspinwall. B. Greene and D. MorrisonCalabi-Yau Moduli Space, Mirror Manifolds and Space-Time Topology Change in String Theory, preprint IASSNS-HEP-93-38: Zbl0899.32006MR1274435
- P. Aspinwall. B. Greene and D. MorrisonThe Monomial-Divisor Mirror Map, preprint IASSNS-HEP-93-43 Zbl0798.14030MR1253648
- [19] P. Berglund, P. Candelas, X. de la Ossa, A. Font, T. Hübsch, D. Jancic and F. Quevedo, Periods for Calabi-Yau and Landau-Ginsburg Vacua, preprint CERN-TH.6865/93: Zbl1009.32500
- P. Berglund, E. Derrich, T. Hübsch and D. Jancic, On Periods for String Compactification. preprint HUPAPP-93-6 Zbl0990.32501
- [20] P. Berglund and S. Katz, Mirror Symmetry for Hypersurfaces in Weighted Projective Space and Topological Couplings, preprint IASSNS-HEP-93-65 Zbl0990.32500MR1282649
- [21] P. Candelas, G. Horowitz, A. Strominger and E. Witten, Nucl. Phys. B258 (1985) 46 MR800347
- [22] Easily accessible introductions to Calabi-Yau manifolds are G. Horowitz, What is a Calabi-Yau Space ? in Unified String Theories, M. Green and D. Gross, editors, World Scientific1986
- P. Candelas, Introduction to Complex Manifolds, Lectures at the 1987 Trieste Spring School, published in the proceedings. For a rigorous mathematical treatment we refer to A.L. Bessis, Einstein Manifolds, Springer1987 MR1034772
- P. Griffiths and J. Harris, Principles of Algebraic Geometry, John Wiley & Sons1978; Zbl0836.14001MR507725
- K. Kodaira, Complex Manifolds and Deformation of Complex Structures, Springer1986 Zbl0581.32012MR815922
- [23] A good and detailed introduction to Calabi-Yau manifolds is the book by T. Hübsch, Calabi-Yau Manifolds. World Scientific1991
- [24] S. T. Yau, Proc. Natl. Acad. Sci.USA74 (1977), 1798; Zbl0355.32028
- S. T. YauComm. Pure Appl. Math.31 (1978) 339 Zbl0369.53059MR480350
- [25] K. Kodaira, L. Nirenberg and D. C. Spencer, Ann. Math.68 (1958) 450 Zbl0088.38004MR112157
- [25] K. Kodaira, L. Nirenberg and D. C. Spencer, Ann. Math.68 (1958) 450 Zbl0088.38004MR112157
- [26] G. Tian, in Mathematical Aspects of String Theory, ed. S. T. Yau, World Scientific, Singapore (1987) Zbl0651.00012MR915812
- [27] A. Strominger, Phys. Rev. Lett.55 (1985) 2547
- A. Strominger in Unified String Theory, eds. M. Green and D. Gross, World Scientific1986; MR849129
- A. Strominger and E. Witten, Comm. Math. Phys.101 (1985) 341 MR815189
- [28] L. Dixon, D. Friedan, E. Martinec and S. Shenker, Nucl. Phys. B282 (1987) 13; MR869937
- S. Hamidi and C. Vafa, Nucl. Phys. B279 (1987) 465; MR867241
- J. Lauer, J. Mas and H. P. NillesNucl. Phys. B351 (1991) 353; MR1093574
- S. Stieberger, D. Jungnickel, J. Lauer and M. Spalinski, Mod. Phys. Lett. A7 (1992) 3859;
- J. Erler, D. Jungnickel, M. Spalinski and S. Stieberger, Nucl. Phys. B397 (1993) 379 MR1219527
- [29] D. Gepner, Phys. Lett.199B (1987) 380 MR929596
- D. Gepner and Nucl. Phys. B311 (1988) 191 MR974275
- [30] J. Distler and B. Greene, Nucl. Phys. B309 (1988) 295 MR967477
- [31] M. Dine, N. Seiberg, X-G. Wen and E. Witten, Nucl. Phys. B278 (1987) 769, Nucl. Phys. B289 (1987) 319 MR895317
- [32] S. Ferrara, D. Lust, A. Shapere and S. Theisen, Phys. Lett.225B (1989) 363 MR1009091
- [33] P. Aspinwall and D. Morrison, Comm. Math. Phys.151 (1993) 245 Zbl0776.53043MR1204770
- [34] E. Witten, Comm. Math. Phys.118 (1988) 411 Zbl0674.58047MR958805
- [35] T. Banks, L. Dixon, D. Friedan and E. Martinec, Nucl. Phys. B284 (1988) 613 MR930976
- [36] M. Ademollo et al., Nucl. Phys. B11 (1976) 77 and Nucl. Phys. B114 (1976) 297 and Phys. Lett.62B (1976) 105
- [37] A. Schwimmer and N. Seiberg, Phys. Lett.184B (1987) 191 MR879234
- [38] M. Dine and N. Seiberg, Nucl. Phys. B301 (1988) 357 MR936751
- [39] E. Witten, Nucl. Phys. B202 (1982) 253;
- R. Rohm and E. Witten, Ann. Phys.17C (1986) 454 MR851628
- [40] P. Candelas, E. Derrick and L. Parkes, Nucl. Phys. B407 (1993) 115 MR1242064
- [41] R. Schimmrigk, Phys. Rev. Lett.70 (1993) 3688 and Kähler manifolds with positive first Chern class and mirrors of rigid Calabi-Yau manifolds, preprint BONN-HE 93-47 MR1220210
- [42] N. Seiberg, Nucl. Phys. B303 (1988) 286 MR953719
- [43] S. Cecotti, S. Ferrara and L. Girardello, Int. J. Mod. Phys. A4 (1989) 2475; MR1017548
- S. Ferrara, Nucl. Phys. (Proc. Suppl.)11 (1989) 342 Zbl0957.81642MR1124909
- [44] P. Candelas, P. Green and T. Hübsch, Connected Calabi-Yau compactifications, in Strings '88, J. Gates et al. (eds), World Scientific1989 Zbl0938.81527
- P. Candelas, P. Green and T. HübschNucl. Phys. B330 (1990) 49;
- T. Hübsch and R. Schimmrigk, Nucl. Phys. B329 (1990) 582
- [45] L. Dixon, V. Kaplunovsky and J. Louis, Nucl. Phys. B329 (1990) 27 MR1036216
- [46] B. de Wit, P. G. Lauwers, R. Philippe, S. Q. Su and A. van Proeyen, Phys. Lett.134B (1984) 37;
- B. de Wit and A. van Proeyen, Nucl. Phys. B245 (1984) 89; MR762191
- J. P. Derendinger, S. Ferrara, A. Masiero and A. van Proeyen, Phys. Lett.140B (1984) 307; MR746903
- B. de Wit, P. G. Lauwers and A. van Proeyen, Nucl. Phys. B255 (1985) 569;
- E. Cremmer, C. Kounnas, A. van Proeyen, J. P. Derendinger, S. Ferrara, B. de Wit and L. Girardello, Nucl. Phys. B250 (1985) 385
- [47] M. Kreuzer and H. Skarke, Nucl. Phys. B388 (1993) 113;
- A. Klemm and R. Schimmrigk, Nucl. Phys. B411 (1994) 559 MR1257839
- [48] P. Candelas, A. Dale, A. Lütken and R. Schimmrigk, Nucl. Phys. B298 (1988) 493;
- P. Candelas, A. Lütken and R. Schimmrigk, Nucl. Phys. B306 (1989) 105
- [49] V. Batyrev and D. van Straten, Generalized Hypergeometric Functions and Rational Curves on Calabi-Yau Complete Intersections in Toric Varieties, preprint 1992 Zbl0843.14016MR1328251
- [50] I. Dolgachev, Weighted Projective Varieties in Lecture Notes in Mathematics956Springer-Verlag (1992) 36 Zbl0516.14014MR704986
- [51] A. R. Fletcher, Working with Weighted Complete Intersections, Max-Planck-Institut Series, No. 35 (1989) Bonn
- [52] D. G. Markushevich, M. A. Olshanetsky and A. M. Perelomov, Comm. Math. Phys.111 (1987) 247 Zbl0628.53065MR899851
- [53] J. Erler and A. Klemm, Comm. Math. Phys.153 (1993) 57 MR1218933
- [54] L. Dixon, J. Harvey, C. Vafa and E. Witten, Nucl. Phys. B261 (1985) 678 MR818423
- L. Dixon, J. Harvey, C. Vafa and E. Witten and Nucl. Phys. B274 (1986) 285 MR851703
- [55] S. S. Roan and S. T. Yau, Acta Math. Sinica (NS)3 (1987) 256; Zbl0649.14024MR916270
- S. S. Roan, J. Diff. Geom.30 (1989) 523 Zbl0661.14031MR1010170
- [56] M. Kreuzer and H. Skarke. Nucl. Phys. B405 (1993) 305;
- M. Kreuzer, Phys. Lett.314B (1993) 31; MR1237377
- A. Niemeyer, Diplom Thesis, TU-München, 1993
- [57] T. Oda, Convex Bodies and Algebraic Geometry: an Introduction to the Theory of Toric Varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, Bd. 15, Springer Verlag1988; Zbl0628.52002MR922894
- V. I. Danilov, Russian Math. Surveys, 33 (1978) 97;
- M. Audin, The Topology of Torus Actions on Symplectic Manifolds, Progress in Mathematics, Birkhäuser1991; Zbl0726.57029MR1106194
- W. Fulton, Introduction to Toric Varieties, Annals of Mathematics Studies, Princeton University Press1993; Zbl0813.14039MR1234037
- V. I. Arnold, S. M. Gusein-Zade and A. N. Varchenko, Singularities of Differntial Maps, Birkhäuser1985, Vol. II, Chapter 8 Zbl1297.32001MR777682
- [58] V. Batyrev, Duke Math. Journal69 (1993) 349 Zbl0812.14035MR1203231
- [59] V. Batyrev, Journal Alg. Geom., to be published
- [60] V. Batyrev, Quantum Cohomology Rings of Toric Manifolds, preprint 1992 Zbl0806.14041MR1265307
- [61] V. Batyrev and D. Cox, On the Hodge Structure of Projective Hypersurfaces in Toric Varieties, preprint 1993 Zbl0851.14021MR1290195
- [62] F. Hirzebruch, Math. Annalen124 (1951) 77 Zbl0043.30302MR45384
- [63] M. Beltrametti and L. Robbiano, Expo. Math.4 (1986) 11. MR879909
- [64] D. Aspinwall, B. Greene and D. Morrison, Phys. Lett.303B (1993) 249
- D. Aspinwall, B. Greene and D. Morrison and The Monomial-Divisor Mirror Map, preprint IASSNS-HEP-93/43 Zbl0798.14030
- [65] S.-S. Roan: Topological Couplings of Calabi-Yau Orbifolds, Max-Planck-Institut Serie No. 22 (1992), to appear in J. of Group Theory in Physics MR1191431
- [66] E. L. Ince, Ordinary Differential Equations, Dover1956 Zbl0063.02971MR10757JFM53.0399.07
- [67] M. Yoshida, Fuchsian Differential Equations, Braunschweig (1987) Vieweg Zbl0618.35001MR986252
- [68] P. A. Griffiths, Bull. Amer. Math. Soc.76 (1970) 228 Zbl0214.19802MR258824
- [69] P. Griffiths, Ann. of Math.90 (1969) 460 MR260733
- [70] P. Candelas, Nucl. Phys. B298 (1988) 458 MR928307
- [71] I. M. Gel'fand, A. V. Zelevinsky and M. M. Kapranov, Func. Anal. Appl.28 (1989) 12
- I. M. Gel'fand, A. V. Zelevinsky and M. M. Kapranov and Adv. Math.84 (1990) 255 MR1080980
- [72] D. Morrison, Where is the Large Radius Limit, preprint IASSNS-HEP-93/68 and Compactifications of Moduli Spaces Inspired by Mirror Symmetry, preprint DUK-M- 93-06
- [73] M. Reid, Decomposition of Toric Morphisms, in Progress in Mathematics36, M. Artin and J. Tate, eds, Birkhäuser1983 Zbl0571.14020MR717617
- [74] S. Ferrara and A. Strominger, in the Proceedings of the Texas A & M Strings '89 Workshop; ed. R. Arnowitt et al., World Scientific1990 Zbl1058.81629MR1148627
- [75] P. Candelas, P. Green and T. HübschNucl. Phys. B330 (1990) 49;
- P. Candelas and X. C. de la Ossa, Nucl. Phys. B355 (1991) 455
- [76] R. Bryant and P. Griffiths, Some observations on the Infinitesimal Period Relations for Regular Threefolds with Trivial Canonical Bundle, in Progress in Mathematics36, M. Artin and J. Tate, eds; Birkhäuser, 1983 Zbl0543.14005MR717607
- [77] A. Strominger, Comm. Math. Phys.133 (1990) 163 Zbl0716.53068MR1071240
- [78] L. Castellani, R. D'Auria and S. Ferrara, Phys. Lett.241B (1990) 57 and Class. Quantum Grav.7 (1990) 1767;
- S. Ferrara and J. Louis, Phys. Lett.278B (1992) 240 MR1159065
- [79] A. Ceresole, R. D'Auria, S. Ferrara, W. Lerche and J. Louis, Int. J. Mod. Phys. A8 (1993) 79 Zbl0802.53055
- [80] X.-G. Wen and E. Witten, Phys. Lett.166B (1986) 397 MR827697
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