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Study of supersymmetric non-linear sigma models

Research Project

Project/Area Number 13640283
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 素粒子・核・宇宙線
Research InstitutionOsaka University

Principal Investigator

HIGASHIJIMA Kiyoshi  Osaka University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (10092313)

Project Period (FY) 2001 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 2003: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2002: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2001: ¥1,000,000 (Direct Cost: ¥1,000,000)
KeywordsNon-linear sigma model / renormalization group / Ricci-flat manifold / auxiliary field formulation / large N method / Einstein-Kahler manifold / 超対称性 / 非線形シグマ模型 / くりこみ群 / Ricci Flat manifold / 補助場の方法 / Large N
Research Abstract

Study of non-linear sigma models is important for several reasons. Two-dimensional non-linear sigma models describe propagation of strings in vurved space-time. It is also a gymnasium for non-perturbative study of difficult phenomena in field theories, like mass generation, bound states problem, dynamical symmetry breaking. It also offers an example of a possible renormalizable field theory that is not renormalizable in perturbation theory. In this project, we proposed
A)Auxiliary field formulation of non-linear sigma models with N=2 supersymmetry.
B)Non-perturbative study of N=2 supersymmetric non-linear sigma models by using the above method
C)Search of conformal field theories by using the renormalization group equation.
D)Study of conformally invariant non-linear sigma models on non-compact manifolds.
We successfully formulated N=2 supersymmetric non-linear sigma models on hermitian symmetric spaces by introducing both D-term and F-term constraints. We applied the large N method to study the non-perturbative phenomena in non-linear sigma models on CP^N and Q^N. We also obtained conformal field theories on non-compact Ricci-flat manifolds constructed as a line bundle Einstein-Kahler manifold. We derived the non-perturbative renormalization group equation for N=2 supersymmetric non-linear sigma models. By solving the fixed point equation, we found new conformal field theories with anomalous dimension.

Report

(4 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • Research Products

    (32 results)

All 2003 2002 2001 Other

All Journal Article (18 results) Publications (14 results)

  • [Journal Article] A New Class of Conformal Field Theories with Anomalous Dimensions2003

    • Author(s)
      Kiyoshi Higashijima, Etsuko Itou
    • Journal Title

      Progress of Theoretical Physics 109巻・5号

      Pages: 751-764

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Journal Article] Unitarity Bound of the Wave Function Renormalization Constant2003

    • Author(s)
      Kiyoshi Higashijima, Etsuko Itou
    • Journal Title

      Progress of Theoretical Physics 110巻・1号

      Pages: 107-114

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Journal Article] Three Dimensional Nonlinear Sigma Models in the Wilsonian Renormalization Method2003

    • Author(s)
      Kiyoshi Higashijima, Etsuko Itou
    • Journal Title

      Progress of Theoretical Physics 110巻・3号

      Pages: 563-578

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Journal Article] Unitarity Bound of the Wave Function Renormalization Constant2003

    • Author(s)
      Kiyoshi Higashijima, Etsuko Itou
    • Journal Title

      Prog.Theor.Phys. 110

      Pages: 107-114

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Journal Article] Three Dimensional Nonlinear Sigma Models in the Wilsonian Renormalization Method2003

    • Author(s)
      Kiyoshi Higashijima, Etsuko Itou
    • Journal Title

      Prog.Theor.Phys. 110

      Pages: 563-578

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Journal Article] Ricci-flat Kahler Manifolds from Supersymmetric Gauge Theories2002

    • Author(s)
      Kiyoshi Higashijima, Tetsuji Kimura, Muneto Nitta
    • Journal Title

      Nuclear Physics B623巻・1-2号

      Pages: 133-149

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Journal Article] Ricci-flat Kahler Manifolds from Supersymmetric Gauge Theories2002

    • Author(s)
      Kiyoshi Higashijima, Tetsuji Kimura, Muneto Nitta
    • Journal Title

      Nuclear Physics B623

      Pages: 133-149

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Journal Article] Gauge Theoretical Construction of Non-compact Calabi-Yau Manifolds2002

    • Author(s)
      Kiyoshi Higashijima, Tetsuji Kimura, Muneto Nitta
    • Journal Title

      Annals of Physics 296 No.2

      Pages: 347-370

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Journal Article] Calabi-Yau Manifolds of Cohomogeneity One as Complex Line Bundles2002

    • Author(s)
      Kiyoshi Higashijima, Tetsuji Kimura, Muneto Nitta
    • Journal Title

      Nuclear Physics B645

      Pages: 438-456

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Journal Article] Normal Coordinates in Kahler Manifolds and the Background Field Method2002

    • Author(s)
      Kiyoshi Higashijima, Etsuko Itou, Muneto Nitta
    • Journal Title

      Prog.Theor.Phys. 108

      Pages: 185-202

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Journal Article] Wilsonian Renormalization Group Approach to N=2 Supersymmetric Sigma Models2002

    • Author(s)
      Kiyoshi Higashijima, Etsuko Itou
    • Journal Title

      Prog.Theor.Phys. 108

      Pages: 737-753

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Journal Article] A New Class of Conformal Field Theories with Anomalous Dimensions2002

    • Author(s)
      Kiyoshi Higashijima, Etsuko Itou
    • Journal Title

      Prog.Theor.Phys. 109

      Pages: 751-764

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Journal Article] Supersymmetric Nonlinear Sigma Models on Ricci Flat Kahler Manifolds with O(N) Symmetry2001

    • Author(s)
      Kiyoshi Higashijima, Tetsuji Kimura, Muneto Nitta
    • Journal Title

      Physics Letters B515巻・3-4号

      Pages: 421-425

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Journal Article] A Note on Conifolds2001

    • Author(s)
      Kiyoshi Higashijima, Tetsuji Kimura, Muneto Nitta
    • Journal Title

      Physics Letters B518巻・3-4号

      Pages: 301-305

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Journal Article] Large N Limit of N=2 Supersymmetric Q^N Model in Two-Dimensions2001

    • Author(s)
      Kiyoshi Higashijima, Tetsuji Kimura, Muneto Nitta, Makoto Tsuzuki
    • Journal Title

      Progress of Theoretical Physics 105

      Pages: 261-285

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Journal Article] Spontaneous Lorentz Symmetry Breaking by Anti-Symmetric Tensor Field2001

    • Author(s)
      Kiyoshi Higashijima, Naoto Yokoi
    • Journal Title

      Physical Review D64,025004

      Pages: 1-8

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Journal Article] Supersymmetric Nonlinear Sigma Models on Ricci Flat Kahler Manifolds with O(N) Symmetry2001

    • Author(s)
      Kiyoshi Higashijima, Tetsuji Kimura, Muneto Nitta
    • Journal Title

      Physics Letters B515

      Pages: 421-425

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Journal Article] A Note on Conifolds2001

    • Author(s)
      Kiyoshi Higashijima, Tetsuji Kimura, Muneto Nitta
    • Journal Title

      Physics Letters B518

      Pages: 301-305

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kiyoshi Higashijima, Tetsuji Kimura, Muneto Nitta: "Construction of Supersymmetric Nonlinear Sigma Models on Noncompact Calabi-Yau Manifolds with Isometry"Proceedings of the 31st International Conference on High Energy Physics, Amsterdam(Elsevier Science B.V.), Eds, S.Bentvelsen et al.. 867-869 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Kiyoshi Higashijima, Etsuko Itou: "A New Class of Conformal Field Theories with Anomalous Dimensions"Progress of Theoretical Physics. 109巻・5号. 751-764 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Kiyoshi Higashijima, Etsuko Itou: "Unitarity Bound of the Wave Function Renormalization Constant"Progress of Theoretical Physics. 110巻・1号. 107-114 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Kiyoshi Higashijima, Etsuko Itou: "Three Dimensional Nonlinear Sigma Models in the Wilsonian Renormalization Method"Progress of Theoretical Physics. 110巻・3号. 563-578 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Kiyoshi Higashijima, Tetsuji Kimura, Muneto Nitta: "Gauge Theoretical Construction of Non-compact Calabi-Yau Manifolds"Annals of Physics. 296巻2号. 347-370 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Kiyoshi Higashijima, Tetsuji Kimura, Muneto Nitta: "Calabi-Yau Manifolds of Cohomogeneity One as Complex Line Bundles"Nuclear Physics. B645巻3号. 438-456 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Kiyoshi Higashijima, Etsuko Itou, Muneto Nitta: "Normal Coordinates in Kahler Manifolds and the Background Field Method"Progress of Theoretical Physics. 108巻1号. 185-202 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Kiyoshi Higashijima, Etsuko Itou: "Wilsonian Renormalization Group Approach to N=2 Supersymmetric Sigma Models"Progress of Theoretical Physics. 108巻4号. 737-753 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Kiyoshi Higashijima, Muneto Nitta: "Kahler Normal Coordinate Expansion in Supersymmetric Theories"Progress of Theoretical Physics. 105巻・2号. 243-260 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Kiyoshi Higashijima他3名: "Large N Limit of N=2 Supersymmetric $Q^N$ Model in Two-Dimensions"Progress of Theoretical Physics. 105巻・2号. 261-285 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Kiyoshi Higashijima, Naoto Yokoi: "Spontaneous Lorentz Symmetry Breaking by Anti-Symmentric Tensor Field"Physical Review. D64巻・025004. 1-8 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Kiyoshi Higashijima, Tetsuji Kimura, Muneto Nitta: "Supersymmetric Nonlinear Sigma Models on Ricci Flat Kahler Manifolds with O(N) Symmetry"Physics Letters. B515巻・3-4号. 421-425 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Kiyoshi Higashijima, Tetsuji Kimura, Muneto Nitta: "A Note on Conifolds"Physics Letters. B518巻・3-4号. 301-305 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Kiyoshi Higashijima, Tetsuji Kimura, Muneto Nitta: "Ricci-flat Kahler Manifolds from Supersymmetric Gauge Theories"Nuclear Physics. B623巻・1-2号. 133-149 (2002)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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