Theoretical and Mathematical Physics

, Volume 109, Issue 3, pp 1544–1555 | Cite as

Multiple Mellin-Barnes integrals as periods of Calabi-Yau manifolds with several moduli

  • M. Passare
  • A. K. Tsikh
  • A. A. Cheshel
Article

Abstract

We give a representation, in terms of iterated Mellin-Barnes integrals, of periods on multi-moduli Calabi-Yau manifolds arising in superstring theory. Using this representation and the theory of multi-dimensional residues, we present a method for analytic continuation of the fundamental period in the form of a Horn series.

Keywords

Manifold Analytic Continuation Fundamental Period Horn Series 

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References

  1. 1.
    T. Hübsch,Calabi-Yau Manifolds—A Bestiary for Physicists, World Scientific, Singapore (1992).Google Scholar
  2. 2.
    P. Berglund, P. Candelas, X. de la Ossa, A. Font, T. Hubsch, D. Jancic, and F. Quevedo,Nucl. Phys. B,419, 352 (1994).Google Scholar
  3. 3.
    P. Candelas, X. de la Ossa, A. Font, S. Katz, and S. R. Morrison,Nucl. Phys. B,416, 481 (1994).Google Scholar
  4. 4.
    P. Candelas, A. Font, S. Katz, and S. R. Morrison, “Mirror symmetry for a two-parameter model-2,” hep-th /9403187.Google Scholar
  5. 5.
    P. Berglund, E. Derrick, T. Hübsch, and D. Janćić, “On periods for string compactifications,” preprint HUPAPP-93/6, IASSNS-HEP-93/80, UTTG-27-93.Google Scholar
  6. 6.
    S. Hosono, A. Klemm, S. Taisen, and S.-T. Yau. “Mirror symmetry, mirror map and application to Calabi Yau hypersurfaces,” hep-th /9308083.Google Scholar
  7. 7.
    P. Candelas, X. de la Ossa, P. Greene, and L. Parkes,Nucl. Phys. B,359, 21 (1991).Google Scholar
  8. 8.
    B. R. Greene and M. R. Plesser,Nucl. Phys.,B338 (1990).Google Scholar
  9. 9.
    V. V. Batyrev,Duke Math. J.,69, 349 (1993).Google Scholar
  10. 10.
    P. Candelas, X. de la Ossa, and S. Katz, “Mirror symmetry for Calabi-Yau hypersurfaces in weightedCP(4) and extensions of Landau-Ginzburg theory,” hep-th /9412117.Google Scholar
  11. 11.
    P. Berglund and S. Katz,Nucl. Phys. B,420, 289 (1994), hep-th /9311014.Google Scholar
  12. 12.
    J. Leray, “Le calcul différentiel et intégral sur une variété analytique complexe (Problème de Cauchy, III),”Bull. Soc. Math. France,87, 81–180 (1959).Google Scholar
  13. 13.
    A. Tsikh,Multi-dimensional Residues and Their Applications, Translations of Mathematical Monographs, Vol. 103, Amer. Math. Soc., Providence, Rhode Island (1992).Google Scholar
  14. 14.
    A. Tsikh, “Methods in the theory of multi-dimensional residues,” Doctoral thesis, Novosibirsk (1990).Google Scholar
  15. 15.
    M. Passare, A. Tsikh, and O. Zhdanov,Aspects of Math. E,26, 233–241 (1994).Google Scholar
  16. 16.
    M. A. Mkrtchyan and A. P. Yuzhakov,Izv. Akad. Nauk Arm. SSR,17, 99–105 (1992).Google Scholar
  17. 17.
    I. M. Gel'fand, A. V. Zelevinsky, and M. M. Kapranov,Funct. Anal. Appl.,28, 94 (1989).Google Scholar
  18. 18.
    A. G. Sveshnikov and A. N. Tikhonov,Theory of Functions of Complex Variables [in Russian], Mir, Moscow (1973).Google Scholar
  19. 19.
    O. I. Marichev,Methods for Computing Integrals of Special Functions [in Russian], Nauka, Minsk (1978).Google Scholar
  20. 20.
    Ph. Griffiths and J. Harris,Principles of Algebraic Geometry, Wiley, New York (1978).Google Scholar
  21. 21.
    E. Elizalde, K. Kirsten, and S. Zerbini, “Applications of the Mellin-Barnes integral representation,” hep-th /9501048.Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • M. Passare
    • 1
  • A. K. Tsikh
    • 2
  • A. A. Cheshel
    • 2
  1. 1.Mathematical InstituteUniversity of StockholmSweden
  2. 2.Krasnoyarsk State UniversityUSSR

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