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Differential equations for periods and super string and susy gauge theories

Research Project

Project/Area Number 09440021
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionKOBE UNIVERSITY

Principal Investigator

YAMADA Yasuhiko  Kobe University Graduate school of Natural Science Associate Professor, 大学院・自然科学研究科, 助教授 (00202383)

Co-Investigator(Kenkyū-buntansha) YANG Sung-Kil  Tsukuba University Faculty of Science Professor, 物理学系, 教授 (70201118)
HOSONO Shinobu  Tokyo University Faculty of Science Associate Professor, 大学院・数理科学科, 助教授 (60212198)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥6,600,000 (Direct Cost: ¥6,600,000)
Fiscal Year 1998: ¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1997: ¥4,500,000 (Direct Cost: ¥4,500,000)
KeywordsSuper symmetry / Seiberg-Witten theory / Period integrals / String thory / Mirror symmetry / Integrability / Painleve equation / Topological field theory / Seiberg-Witten 理論 / Painleve 方程式 / Calabi-Yau多様体 / プレポテンシャル / 可積分系 / 特異点理論
Research Abstract

In this project, each of the three investigators carried out his research independently with in close co-operation. Inspiring with each other, we can obtain successful results more than our initial aim.
1. Y.Yamada studied the relation between the integrable structure in the two dimensional quantum gravity and singularity theories. He found deep connections between the KP equations, Drinfeld-Sokolov equations and Painleve equations, and obtained successful results on the theory of Painleve equations and their symmetries. This result is expected to be applied to other problems in mathematical physics.
2. S.K.Yang investigated the Seiberg-Witten curves (or more general geometries) in N = 2 susy gauge theories in systematic way with explicit examples. He clarify the profound relation with the singularity theories and determine the geometrical structures for exceptional gauge groups.
3. S.Hosono has continued the research on the mirror symmetry. He made important contribution for the evaluation of the Gromov-Witten invariants for elliptic- or K3-fibered Calabi-Yau manifolds. There is also some progress in counting the higher genus curves from theoretical and computing points of view.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (42 results)

All Other

All Publications (42 results)

  • [Publications] Masatoshi Noumi: "Notes on the flat structures associated with simple and simply elliptic singularities" Intergrable systems and algebraic geometry,(eds. M.Saito et.al.). 373-383 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Masatoshi Noumi: "Affine Weyl groups, discrete dynamical systems and Painleve^^, equations" Comm.Math.Phys.199. 281-295 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Masatoshi Noumi: "Umemura polynomials for Painleve^^, V equation" Phys.Lett.A247. 65-69 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Masatoshi Noumi: "Higher order Painleve^^, equations of type A^<(1)>_ι" Funkicialaj Ekvacioj. 41. 408-503 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Masatoshi Noumi: "Symmetries in the fourth Painleve^^, equation and Okamoto polynomials" Nagoya Math.J.(印刷中). (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Yasuhiko Yamada: "Determinant formulas for the generalized Painleve^^,equations of type A" Nagoya Math.J.(印刷中). (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Seiji Terashima: "Seiberg-Witten Geometry with Various Matter Contents" Nucl.Phys.B537. 344-360 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Katsushi Ito: "Seiberg-Witten Theory as d<1 Topological Strings" Phys.Lett.B441. 155-162 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hiroaki Kanno: "Donaldson-Witten Functions of Massless N=2 Supersymmetric QCD" Nucl.Phys.B535. 512-530 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Seiji Terashima: "Exceptional Seiberg-Witten Geometry with Massive Fundamental Matters" Phys.Lett.B430. 102-108 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Shinobu Hosono: "GKZ systems, Groebner fans, and moduli space of Calabi-Yau hypersurfaces" Progr.Math.160. 239-265 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Masatoshi Noumi: "Notes on the flat structures associ-ated with simple and simply elliptic singularities" Integrable systems and algebraic geometry, (eds.M.Saito et.al.) World Scientific. 373-383 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Noumi and Y.Yamada: "Affine Weyl groups, discrete dynamical systems and Painleve equations" Comm.Math.Phys.199. 281-295 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Noumi and Y.Yamada: "Umemura polynomials for Painleve V equation" Phys.Lett.A247. 65-69 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Noumi and Y.Yamada: "Higher order Painleve equa-tions of type A_1^<(1)>" Funkcialaj Ekvacioj. 41. 408-503 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Noumi and Y.Yamada: "Symmetries in the fourth Painleve equation and Okamoto polynomials" Nagoya Math.J.(in press). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Yasuhiko Yamada: "Determinant formulas for the gener-alized Painleve equations of type A" Nagoya Math.J.(in press). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Terashima and S.K.-Yang: "Seiberg-Witten Geome-try with Various Matter Contents" Nucl.Phys.B537. 344-360 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Ito and S.K.-Yang: "Seiberg-Witten Theory as d < 1 Topological Strings" Phys.Lett.B441. 155-162 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Kanno and S.K.-Yang: "Donaldson-Witten Functions of Massless N = 2 Supersymmetric QCD" Nucl.Phys.B535. 512-530 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Terashima and S.K.-Yang: "Exceptional Seiberg-Witten Geometry with Massive Fundamental Matters" Phys.Lett.B430. 102-108 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Shinobu Hosono: "GKZ systems, Groebner fans, and moduli space of Calabi-Yau hypersurfaces" Progr.Math.160. 239-265 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Masatoshi Noumi: "Notes on the flat structures associated with simple and simply elliptic singularities" Integrable systems and algebraic geometry,(eds.M.Saito et.al.) World Scientific. 373-383 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Masatoshi Noumi: "A ffine Weyl groups,discrete dynamical systems and Painleve equations" Comm.Math.Phys.199. 281-295 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Masatoshi Noumi: "Umemura polynomials for Painleve V equation" Phys.Lett.A247. 65-69 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Masatoshi Noumi: "Higher order Painleve equations of type A^<(1)>_l" Funkcialaj Ekvacioj. 41. 408-503 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Masatoshi Noumi: "Symmetries in the fourth Painleve equation and Okamoto polynomials" Nagoya Math.J.(印刷中). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Yasuhiko Yamada: "Determinant formulas for the generalized Painleve equations of type A" Nagoya Math.J.(印刷中). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Seiji Terashima: "Seiberg-Witten Geometry with Various Matter Contents" Nucl.Phys.B537. 344-360 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Katsushi Ito: "Seiberg-Witten Theory as d<1 Topological Strings" Phys.Lett.B441. 155-162 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Hiroaki Kanno: "Donaldson-Witten Functions of Massless N=2 Supersymmetric QCD" Nucl.Phys.B535. 512-530 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Seiji Terashima: "Exceptional Seiberg-Witten Geometry with Massive Fundamental Matters" Phys.Lett.B430. 102-108 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Shinobu Hosono: "GKZ systems,Groebner fans,and moduli space of Calabi-Yau hypersurfaces" Progr.Math.160. 239-265 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Noumi and Y.Yamada: "Notes on the dispersioless hierarchies associated with simple and simply elliptic singularities" Proceedings of Taniguchi Symposium 1997 “Integrablo Systems and Algebraic Geometry". (掲載予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] M.Noumi and Y.Yamada: "Symmetries in the fourth Painleve equation and Okamoto polynomials" Nagoya Methematical Journal.(掲載予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] S.Terasima and S-K,Yang: "ADE Confining Phase Superpotentials" Nucl.Phys.B. (掲載予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] K.Ito and S-K,Yang: "Flat Coordinates, Topological Landau-Giuzburg Models and the Seiborg-Vitten Period integrals" Physics Letters. B415. 45-53 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] S-K,Yang: "Non-perturbative Aspects of N=2 Supersymmretric Gauge Theones" Prog.Theor-Phys.A. (掲載予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] S-K,Yang and K.Ito: "A-D-E Singularity and Prepotentials in N=2 Suporsymmetric Yang-Mills Theory" Jnt.J.Mod.Phys A. (掲載予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] S.Hosono, M.Saito and J.Stienstra: "On the Mirror Gymmetry Conjecture for the schoen's Calabi-Yau 3-folds" Proceedings of Taniguchi Symposium 1997 “Tutegrable systems and Algebraic Geometry". (掲載予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] S.Hosono: "GK2 systems, Grbbner Faus and Modali space of Calabi-Yau Hyper surfaces" Progress in Mathematics, Birkhanser. (印刷中).

    • Related Report
      1997 Annual Research Report
  • [Publications] S.Hosono, B.H.Lian and S.-T.Yau: "Maximal Degeneracy Points of GKZ Systems" J.of Amer.Math.Soc.10. 427-443 (1997)

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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