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Geometry of manifold of special holonomy and gauge theory/gravity correspondence

Research Project

Project/Area Number 14540073
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

KANNO Hiroaki  Nagoya University, Grad.School of Math., Professor, 大学院・多元数理科学研究科, 教授 (90211870)

Co-Investigator(Kenkyū-buntansha) OHTA Hiroshi  Nagoya University, Grad.School of Math., Ass.Professor, 大学院・多元数理科学研究科, 助教授 (50223839)
YASUI Yukinori  Osaka City Univ., Grad.School of Sci., Ass.Professor, 大学院・理学研究科, 助教授 (30191117)
Project Period (FY) 2002 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2004: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,300,000 (Direct Cost: ¥1,300,000)
Keywordsexceptional holonomy / gauge theory / gravity correspondence / instanton / topological string / Seiberg-Witten theory / D-brane / 重力対応 / 超対称ゲージ理論 / D-ブレイン / 行列模型 / Gromov-Witten不変量 / 例外的ホロノミー群 / M理論 / ALC計量
Research Abstract

D-branes in superstring theory provide a new method of investigating the mathematical structure of gauge theory. For example, D-branes in manifolds of exceptional holonomy group G_2,Spin(7) describe non-perturbative dynamics of supersymmetric gauge theory. In collaboration with Y.Yasui, we constructed explicit metrics of Spin(7) holonomy, that are of cohomogeneity one with SU(3)/U(1) principal orbit. In particular we found a new type of metrics that has asymptotically a circle S^1 of finite radius. This is a higher dimensional analog of four dimensional gravitational instantons ; Taub-NUT metic and Atiyah-Hitchin metic. We expect these metrics have some applications to M theory compactification.
One of aims of string theory is a unification of gauge theory and gravity and gauge theory/gravity correspondence has been attracted much attention recently. When we consider topological gauge/string theory, the correspondence can be formulated mathematically more rigorous way. One of recent important achievements is instanton counting in four dimensional gauge theory by Nekrasov. In collaboration with T.Eguchi, we show that Nekrasov's partition function of instanton counting can be reproduced as a partition function of topological string theory. The partition function for SU(N) Seiberg-Witten theory is obtained by considering topological string whose target space is the ALE fibration of type A_{N-1} over P^1. Matter field can be incorporated by making a blow up on the target space. The methods used in this computation have close relations to various branches in mathematics, such as representation theory, combinatorics, knot theory and integrable systems.

Report

(4 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (36 results)

All 2005 2004 2003 2002 Other

All Journal Article (29 results) Publications (7 results)

  • [Journal Article] Simple Singularities and Symplectic Fillings2005

    • Author(s)
      H.Ohta, K.Ono
    • Journal Title

      Journal of Differential Geometry 発表予定

    • Related Report
      2004 Annual Research Report
  • [Journal Article] New Infinite Series of Einstein Metrics on Sphere Bundles from AdS Black Holes2005

    • Author(s)
      Y.Hashimato, M.Sakaguchi, Y.Yasui
    • Journal Title

      Communications in mathematical Physics 発表予定

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Geometric Transitions, Chern-Simons Gauge Theory and Veneziano Type Amplitudes2004

    • Author(s)
      T.Eguchi, H.Kanno
    • Journal Title

      Physics Letters B 585

      Pages: 163-172

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] Whitham Prepotemtial and Superpotential2004

    • Author(s)
      H.Itoyama, H.Kanno
    • Journal Title

      Nuclear Physics B 686

      Pages: 155-164

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Properties of some five dimensional Eiinstein matrics2004

    • Author(s)
      G.W.Gibbons, S.A.Hartnoll, Y.Yasui
    • Journal Title

      Class.Quant.Grav. 21

      Pages: 4697-4730

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Geometric transitions, Chem-Simons gauge theory and Veneziano type amplitudes2004

    • Author(s)
      T.Eguchi, H.Kanno
    • Journal Title

      Phys.Lett., B 585

      Pages: 163-172

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Whitham Prepotential and Superpotential2004

    • Author(s)
      H.Itoyama, H.Kanno
    • Journal Title

      Nucl.Phys., B 686

      Pages: 155-164

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Properties of some five dimensional Einstein metrics2004

    • Author(s)
      G.W.Gibbons, S.A.Hartnoll, Y.Yasui
    • Journal Title

      Class.Quant Grav. 21

      Pages: 4697-4730

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Whitham Prepotential and Superpotential2004

    • Author(s)
      H.Itoyama, H.Kanno
    • Journal Title

      Nuclear Physics B 686

      Pages: 155-164

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Properties of Some Five Dimensional Einstein Metric2004

    • Author(s)
      G.W.Gibbons, S.A.Hartnoll, Y.Yasui
    • Journal Title

      Classical and Quantum Gravity 21

      Pages: 4697-4730

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Harmonic Forms and Deformation of ALC metrics with Spin(7) Holonomy2003

    • Author(s)
      H.Kanno, Y.Yasui
    • Journal Title

      Nuclear Physics B 650

      Pages: 449-474

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Supereigenvalue Model and Dijkgraaf-Vafa Proposal2003

    • Author(s)
      H.Itoyama, H.Kanno
    • Journal Title

      Physics Letters B 573

      Pages: 227-234

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Topological Strings and Nekrasov's Formulas2003

    • Author(s)
      T.Eguchi, H.Kanno
    • Journal Title

      Journal of High Energy Physics 12

      Pages: 6-6

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Symplectic fillings of the link of simple elliptic singularities2003

    • Author(s)
      H.Ohta, K.Ono
    • Journal Title

      J.Reine Angew.Math. 565

      Pages: 183-205

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Compact Einstein Spaces based on Quaternionic Kahler Manifolds2003

    • Author(s)
      Y.Hiragane, H.Ishihara, Y.Yasui
    • Journal Title

      Class.Quant.Grav. 20

      Pages: 3933-3950

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Harmonic Forms and Deformation of ALC metrics with Spin(7) Holonomy2003

    • Author(s)
      H.Kanno, Y.Yasui
    • Journal Title

      Nucl.Phys., B 650

      Pages: 449-474

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Supereigenvalue Model and Dijkgraaf-Vafa Proposal2003

    • Author(s)
      H.Itoyama, H.Kanno
    • Journal Title

      Phys.Lett., B 573

      Pages: 227-234

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Topological Strings and Nekrasov's Formulas2003

    • Author(s)
      T.Eguchi, H.Kanno
    • Journal Title

      JHEP 12

      Pages: 6-6

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Symptectfc fillings of the fink of simple elliptic singularities2003

    • Author(s)
      H.Ohta, K.Ono
    • Journal Title

      J.Reine Angew.Math. 565

      Pages: 183-205

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Compact Einstein Spaces based on Quatemionic Kahler Manifolds2003

    • Author(s)
      M.Hiragane.H.Ishihara, Y.Yasui
    • Journal Title

      Class.Quant Grav. 20

      Pages: 3933-3950

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On Spin(7) Holonomy Metric Based on SU(3)/U(1)2002

    • Author(s)
      H.Kanno, Y.Yasui
    • Journal Title

      Journal of Geometry and Physics 43

      Pages: 293-309

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On Spin(7) Holonomy Metric Based on SU(3)/U(1) : II2002

    • Author(s)
      H.Kanno, Y.Yasui
    • Journal Title

      Journal of Geometry and Physics 43

      Pages: 310-326

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Brieskorn manifolds and metrics of positive scalar curvature2002

    • Author(s)
      H.Ohta
    • Journal Title

      Adv.Studies Pure Math. 34

      Pages: 231-236

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On Spin(7) Holonomy Metric Based on SU(3)/U(1)2002

    • Author(s)
      H.Kanno, Y.Yasui
    • Journal Title

      J.Geom.Phys. 43

      Pages: 293-309

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On Spin(7) Holonomy Metric Based on SU(3)/U(1) : II2002

    • Author(s)
      H.Kanno, Y.Yasui
    • Journal Title

      J.Geom.Phys. 43

      Pages: 310-326

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Simple Singularities and Symplectic Fillings

    • Author(s)
      H.Ohta, K.Ono
    • Journal Title

      Journal of Differential Geometry (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] New Infinite Series of Einstein Metrics on Sphere Bundles from Ads Black Holes

    • Author(s)
      M.Hashimoto, M.Sakaguchi, Y.Yasui
    • Journal Title

      Commun.Math.Phys. (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Simple singularities and symplectic fillings

    • Author(s)
      H.Ohta, K.Ono
    • Journal Title

      J.Differential Geom. (in press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] New Infinite Series of Einstein Metrics on Sphere Bundles from Ads Black Holes

    • Author(s)
      Y.Hashimoto, M.Sakaguchi, Y.Yasui
    • Journal Title

      Comm.Math.Phys. (in press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Publications] H.Kanno, Y.Yasui: "Harmonic Forms and Deformation of ALC metric with Spin(7) Holonomy"Nuclear Physics B. 650. 449-474 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Itoyama, H.Kanno: "Supereigenvalue Model and Dijkgraaf-Vafa Proposal"Physics Letters B. 573. 227-234 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Eguchi, H.Kanno: "Topological Strings and Nekrasov's Formulas"Journal of High Energy Physics. 12. 006 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Eguchi, H.Kanno: "Geometric Transitions, Chern-Simons Gauge Theory and Veneziano Type Amplitudes"Physics Letters B. (発表予定). (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Kanno, Y.Yasui: "On Spin(7) Holonomy Metric Based on SU(3)/U(1)"Journal of Geometry and Physics. 43. 293-309 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] H.Kanno, Y.Yasui: "On Spin(7) Holonomy Metric Based on SU(3)/U(1) : II"Journal of Geometry and Physics. 43. 310-326 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] H.Kanno, Y.Yasui: "Harmonic Forms and Deformation of ALC metrics with Spin(7) Holonomy"Nuclear Physics B. (発表予定). (2003)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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