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Duality and modular form in topological gauge theory

Research Project

Project/Area Number 10640081
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionHiroshima University

Principal Investigator

KANNO Hiroaki  Hiroshima Univ., Faculty of Science, Associate Professor, 理学部, 助教授 (90211870)

Project Period (FY) 1998 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 1999: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1998: ¥1,700,000 (Direct Cost: ¥1,700,000)
KeywordsInstanton / Topological gauge theory / Special holonomy group / Supersymmetric cycle / 超対称ゲージ理論 / 位相的場の量子論 / Seiberg-Witten 理論
Research Abstract

From the viewpoint of non-perturbative dynamics of supersymmetric gauge theory and dualities of superstring theory we have investigated the geometry of instanton moduli space in higher dimensions and its relation to supersymmetric cycles, which are naturally introduced on the manifold of special holonomy.
We first argued that supersyrnmetric cycles play a significant role in the problem of compactifying the instanton moduli space in higher dimensions. As an explicit example we constructed the octonionic instanton solutions on a non-compact eight-dimensional manifold with Spin (7) holonomy. However, our understanding of the geometry of its moduli space is still incomplete and it is an open problem to construct a new kind of topological invariants based on the octonionic instanton moduli space.
Quite recently a substantial progress has been made in the five dimensional supersymmetric gauge theory compactified on a circle, which was the research subject in 1998. It seems possible to understand the space-time instanton in topological gauge theory from the world-sheet instanton of string theory in which the mirror symmetry gives a powerful tool.

Report

(3 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • Research Products

    (8 results)

All Other

All Publications (8 results)

  • [Publications] H.KANNO: "A Note on Higher Dimensional Instantons and Supersymmetric Cycles"Progress of Theoretical Physics Supplement. 135. 18-28 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H.KANNO et al.: "Yang-Mills Instanton on Luaterninic Kine Bundle of Spin(7) Holonomy"Jounal of Geometry and Physics. (発表決定). (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Kanno: "A note on higher dimensional instantons and supersymmetric cycles"Prog. Theor. Phys. 135. 18-28 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Kanno and Y. Yasui: "Yang-Mills instantons on quaternionic line bundle of Spin(7) holonomy"J. Geom. Phys.. (to be published).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H.KANNO: "A Note on Higher Dimensional Instantons and Supersymmetic Cycles"Progress.of Theoretical Physics Supplement. 135. 18-28 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H.KANNO,et.al.: "Yang-Mills Instanton on Quaternionic:Line Bundle of Spin(7) Holonomy"Journal of Geometry and Physics. (発表予定). (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] H.Kannno: "Picard-Fuchs Equations and Prepotential of Five Dimensional SUSY Gauge Theory Compactified on a Circle" Nuclear Physics. 530. 73-98 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Kanno: "Donaldson-Witten Function of Massless N=2 Supersymmetric QCD" Nuclear Physics B. 535. 512-530 (1998)

    • Related Report
      1998 Annual Research Report

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Published: 1998-04-01   Modified: 2016-04-21  

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