Geodesic
Target Space Duality of Calabi–Yau Spaces with Two Moduli
Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 3, pp. 358-374 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the context of superstring compactifications on Calabi–Yau threefolds, we consider the Picard–Fuchs equations that are obeyed by the periods of the holomorphic three-form. We review, focusing on an example with two moduli, some powerful algebro-geometric techniques for computing the monodromy group of these equations, which is closely related to the target space duality group. For the example investigated, the latter is shown to be given by a three-dimensional representation of a central extension of $B_5$, the braid group on five strands. 
@article{TMF_1994_98_3_a5,
     author = {A. Ceresole},
     title = {Target {Space} {Duality} of {Calabi{\textendash}Yau} {Spaces} with {Two} {Moduli}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {358--374},
     year = {1994},
     volume = {98},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_98_3_a5/}
}
TY  - JOUR
AU  - A. Ceresole
TI  - Target Space Duality of Calabi–Yau Spaces with Two Moduli
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1994
SP  - 358
EP  - 374
VL  - 98
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1994_98_3_a5/
LA  - ru
ID  - TMF_1994_98_3_a5
ER  - 
%0 Journal Article
%A A. Ceresole
%T Target Space Duality of Calabi–Yau Spaces with Two Moduli
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1994
%P 358-374
%V 98
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1994_98_3_a5/
%G ru
%F TMF_1994_98_3_a5
A. Ceresole. Target Space Duality of Calabi–Yau Spaces with Two Moduli. Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 3, pp. 358-374. http://geodesic.mathdoc.fr/item/TMF_1994_98_3_a5/

[1] A. Ceresole, R. D'Auria, T. Regge, Duality Group for Calabi-Yau two-Moduli Space, preprint POLFIS TH. 05/93, DFTT 34/93 ; Nuclear Phys. B, 414:1–2 (1994), 517–537 | MR | DOI | Zbl

[2] P. Candelas, G. Horowitz, A. Strominger, A. Witten, Nucl. Phys. B, 268 (1985), 46 ; M. Green, J. Schwarz, E. Witten, Superstring Theory, Univ. Press, Cambridge, 1987 | DOI | MR | MR

[3] P. Candelas, X. C. de la Ossa, Nucl. Phys. B, 355 (1991), 455 | DOI | MR | Zbl

[4] S. Cecotti, S. Ferrara, L. Girardello, Int. J. Mod. Phys. A, 4 (1989), 2475 ; Phys. Lett. B, 213 (1988), 443 | DOI | MR | Zbl | DOI | MR

[5] L. J. Dixon, V. S. Kaplunovsky, J. Louis, Nucl. Phys. B, 329 (1990), 27 | DOI | MR

[6] W. Lerche, C. Vafa, N. P. Warner, Nucl. Phys. B, 324 (1989), 427 ; B. Greene, M. Plesser, Nucl. Phys. B, 338 (1990), 15 ; P. Candelas, M. Lynker, R. Schimmrigk, Nucl. Phys. B, 341 (1990), 383 ; P. Berglund, T. Hübsch, Nucl. Phys. B, 393 (1993), 377 ; P. Berglund, S. Katz, Mirror Symmetry for Hypersurfaces in Weighted Projective Space and Topological Couplings, preprint IASSNS-HEP-93/65, NSF-ITP-93-128, OSU-M-93-2, UTTG-24-93 | DOI | MR | DOI | MR | DOI | MR | Zbl | DOI | MR | Zbl | MR

[7] P. Candelas, X. C. de la Ossa, P. S. Green, L. Parkes, Phys. Lett. B, 258 (1991), 118 | DOI | MR

[8] P. Aspinwall, D. Morrison, Comm. Math. Phys., 151 (1993), 245 ; E. Witten, Essays on Mirror Manifolds, ed. S. T. Yau, Intenational Press, 1992 | DOI | MR | Zbl | MR

[9] E. Witten, Nucl. Phys. B, 403 (1993), 159 ; P. S. Aspinwall, B. R. Greene, D. R. Morrison, Phys. Lett., 303 (1993), 249 ; Calabi-Yau Moduli Space, mirror manifolds and spacetime topology change in string theory, preprint IASSNS-HEP-93/38, CLNS-93/1236 | DOI | MR | Zbl | DOI | MR

[10] B. de Wit, A. van Proeyen, Nucl. Phys. B, 245 (1984), 89 ; B. de Wit, P. Lauwers, A. van Proeyen, Nucl. Phys. B, 255 (1985), 569 ; E. Cremmer, C. Kounnas, A. van Proeyen, J. P. Derendinger, S. Ferrara, B. de Wit, L. Girardello, Nucl. Phys. B, 250 (1985), 385 | DOI | MR | DOI | DOI | MR

[11] S. Ferrara, A. Strominger, “$N=2$ spacetime supersymmtry and Calabi-Yau moduli space”, Strings '89 (College Station, TX, 1989), World Sci. Publ., River Edge, NJ, 1990, 245–252 ; S. Cecotti, Comm. Math. Phys., 124 (1989), 23 ; A. Cadavid, M. Bodner, S. Ferrara, Phys. Lett. B, 247 (1991), 25 | MR | DOI | MR | Zbl | MR

[12] A. Strominger, Comm. Math. Phys., 133 (1990), 163 | DOI | MR | Zbl

[13] P. Candelas, X. C. de la Ossa, Nucl. Phys. B, 355 (1991), 455 | DOI | MR | Zbl

[14] L. Castellani, R. D'Auria, S. Ferrara, Phys. Lett. B, 241 (1990), 57 ; Class. Quant. Grav., 1 (1990), 317; R. D'Auria, S. Ferrara, P. Fré, Nucl. Phys. B, 359 (1991), 705 | DOI | MR | DOI | MR

[15] A. Cadavid, S. Ferrara, Phys. Lett. B, 267 (1991), 193 | DOI | MR

[16] W. Lerche, D. Smit, N. Warner, Nucl. Phys. B, 372 (1992), 87 | DOI | MR

[17] D. Morrison, Essays on Mirror manifolds, ed. S. T. Yau Editor, Intenational Press, 1992 ; A. Font, Nucl. Phys. B, 391 (1993), 358 ; A. Klemm, S. Theisen, Nucl. Phys. B, 389 (1993), 153 | MR | DOI | MR | Zbl | DOI | MR

[18] R. Dijkgraaf, E. Verlinde, H. Verlinde, Nucl. Phys. B, 352 (1991), 59 | DOI | MR

[19] E. Verlinde, N. P. Warner, Phys. Lett. B, 269 (1991), 96 ; Z. Maassarani, Phys. Lett. B, 273 (1991), 457 ; A. Klemm, M. G. Schmidt, S. Theisen, Int. J. Mod. Phys. A, 1992, no. 7, 6215 | DOI | MR | DOI | MR | DOI | MR | Zbl

[20] S. Cecotti, C. Vafa, Nucl. Phys. B, 367 (1991), 359 | DOI | MR | Zbl

[21] S. Ferrara, J. Louis, Phys. Lett. B, 278 (1992), 240 | DOI | MR

[22] A. Ceresole, R. D'Auria, S. Ferrara, W. Lerche, J. Louis, Int. J. Mod. Phys. A, 8 (1993), 79 | DOI | MR | Zbl

[23] M. Bershadsky, S. Cecotti, H. Ooguri, C. Vafa, Harvard preprints HUTP-93/A008, HUTP-93/A025

[24] P. Candelas, X. C. de la Ossa, A. Font, S. Katz, D. Morrison, Mirror Symmetry for Two Parameter Models 1, preprint CERN-TH.6884/93, UTTG-15-93, NEIP-93-005, OSU-M-93-1

[25] P. Berglund, P. Candelas, X. de la Ossa, A. Font, T. Hubsch, D. Jancic, F. Quevedo, Periods for Calabi-Yau and Landau-Ginzburg Vacua, preprint CERN-TH. 6865/93,HUPAPP-93/3, NEIP 93-004, NSF-ITP-93-96, UTTG-13-93 | MR

[26] S. Hosono, A. Klemm, S. Theisen, S. T. Yau, Mirror Symmetry, Mirror Map and Applications to Calabi-Yau Hypersurfaces, preprint HUTMP-93/0801 and LMU-TPW-93-22 | MR

[27] D. Morrison, Essays on Mirror Manifolds, ed. S. T. Yau, Intenational Press, 1992 | MR

[28] P. Griffiths, Ann. Math., 90 (1969), 460 | DOI | MR | Zbl

[29] P. Candelas Nucl. Phys. B, 298 (1988), 458 | DOI | MR

[30] B. Blok, A. Varchenko, Int. J. Mod. Phys. A, 7 (1992), 1467 | DOI | MR | Zbl

[31] K. Kikkawa, M. Yamasaki, Phys. Lett. B, 149 (1984), 357 ; N. Sakai, L. Senda, Progr. Theor. Phys., 75 (1986), 692 ; V. P. Nair, A. Shapere, A. Strominger, F. Wilczek, Nucl. Phys. B, 287 (1987), 402 ; A. Giveon, E. Rabinovici, G. Veneziano, Nucl. Phys. B, 322 (1989), 167 ; A. Shapere, F. Wilczek, Nucl. Phys. B, 320 (1989), 167 ; M. Dine, P. Huet, N. Seiberg, Nucl. Phys. B, 322 (1989), 301 ; J. Molera, B. Ovrut, Phys. Rev. D, 40 (1989), 1150 ; J. Lauer, J. Maas, H. P. Nilles, Phys. Lett. B, 226 (1989), 25 ; Nucl. Phys. B, 351 (1991), 353 ; W. Lerche, D. Lust, N. P. Warner, Phys. Lett. B, 231 (1989), 418 ; M. Duff, Nucl. Phys. B, 335 (1990), 610 ; A. Giveon, M. Porrati, Phys. Lett. B, 246 (1990), 54 ; Nucl. Phys. B, 355 (1991), 422 ; Giveon, N. Malkin, E. Rabinovici, Phys. Lett. B, 238 (1990), 57 ; J. Erler, D. Jungnickel, H. P. Nilles, preprint MPI-Ph/91-90; S. Ferrara, D. Lüst, A. Shapere, S. Theisen, Phys. Lett. B, 233 (1989), 147 ; J. Schwarz, Caltech preprint CALT-68-1581, 1990; Phys. Lett. B, 272 (1991), 239 ; Strings: Stony Brook, World Scientific, 1991 | DOI | MR | DOI | MR | DOI | MR | DOI | MR | DOI | MR | DOI | MR | DOI | MR | DOI | MR | DOI | MR | DOI | MR | DOI | MR | Zbl | DOI | MR | DOI | MR | DOI | MR | DOI | MR | DOI | MR

[32] R. D'Auria, S. Ferrara, String Quantum Symmetries from Picard-Fuchs Equations and their Monodromy, preprint CERN-TH.6777/93, POLFIS-TH.24/93 ; Ann. Physics, 231:1 (1994), 84–109 | MR | Zbl | DOI | Zbl

[33] T. Regge, “The Fundamental Group Of Poincare And The Analytic Properties Of Feynman Relativistic Amplitudes”, Nobel Symposium, VIII, 1968 | MR

[34] G. Ponzano, T. Regge, E. R. Speer, M. J. Westwater, Comm. Math. Phys., 15 (1969), 83 ; Comm. Math. Phys., 18 (1970), 1 | DOI | MR | Zbl | DOI | MR | Zbl

[35] E. Cremmer, A. Van Proyen, Class. Quantum Grav., 2 (1985), 445 | DOI | MR | Zbl

[36] O. Zariski, Algebraic Surfaces, II ed., Springer-Verlag, 1971 | MR | Zbl

[37] O. Zariski, Ann. for Math., 38 (1937), 131 | DOI | MR

[38] E. R. van Kampen, Amer. J. Math., 55 (1933), 255 | DOI | MR

[39] V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko, Singularities of Differentiable Maps, vol. II, Monographs in Mathematics, 83, Birkhäuser Boston Inc., Boston, MA, 1988 | MR | Zbl