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String Theory, Matrix Models and Noncommutative Geometry

Research Project

Project/Area Number 13640308
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 InstitutionUniversity of Tsukuba (2002-2004)
The High Energy Accelerator Research Organization (2001)

Principal Investigator

ISHIBASHI Nobuyuki  University of Tsukuba, Graduate School of Pure and Applied Sciences, Professor, 大学院・数理物質科学研究科, 教授 (70211729)

Project Period (FY) 2001 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2004: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2003: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2002: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2001: ¥800,000 (Direct Cost: ¥800,000)
KeywordsString theory / D-brane / Membrane theory / M theory / Noncritical Strings / Two dimensional quantum gravity / Nonperturbative effects / String field theory / 行列模型 / D-instanton / D-ブレーン / 超弦理論 / ブレーン / 膜
Research Abstract

Superstring theory has been actively studied as a candidate for the unified theory of all the fundamental interactions including gravity. However, the fundamental formulation of the theory is not so well established. The perturbation theory is understood fairly well, but the construction of the field theory of strings is far from being completed. Because of this, we do not understand the fundamental symmetry of the theory and it is difficult to construct the model of elementary particles using this theory. As a fundamental formulation of string theory, matrix models are string theory which are not obvious when we consider the theory as a theory of strings. In this research, we studied the matrix models from the following points of view.
Firstly we studied the membrane theory. The strong coupling limit of Type IIA string theory is considered to be described by a theory called M-theory. M-theory can be described as a theory of membranes. Recently, it is proposed that the membrane theory can be described as a matrix quantum mechanics. In this research we studied the matrix quantum mechanics and discuss the worldvolume symmetry of the membranes.
Another topic we studied is the noncritical string theory. Noncritical string theory is a string theory in a spacetime with dimension less than 1.Such a string theory can be exactly solved by matrix model approach. It is used as a toy model for the critical ones, especially useful in studying the nonperturbative aspects of string theory. The nonperturbative effects in noncritical string theory are regarded as due to D-instantons. In this research we calculated the chemical potential of these instantons and showed that its value is a universal quantity independent of the method of regularization.

Report

(5 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • Research Products

    (12 results)

All 2004 2002 2001 Other

All Journal Article (11 results) Publications (1 results)

  • [Journal Article] Loop versus Matrices : The Nonperturbative Aspects of Noncritical String2004

    • Author(s)
      N.Hanada, N.Ishibashi et al.
    • Journal Title

      Progress of Theoretical Physics 112

      Pages: 131-181

    • NAID

      110001196193

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Perturbative Dynamics of Matrix String for the Membrane2004

    • Author(s)
      M.Hayakawa, N.Ishibashi
    • Journal Title

      JHEP 0404

      Pages: 47-47

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Loops versus Matrices : The Nonperturbative Aspects of Noncritical String2004

    • Author(s)
      N.Hanada, M.Hayakawa, N.Ishibashi, H.Kawai, T.Kuroki, Y.Matsuo, T.Tada
    • Journal Title

      Progress Theoretical Physics 112

      Pages: 131-181

    • NAID

      110001196193

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Perturbative Dynamics of Matrix String for the Membrane2004

    • Author(s)
      M.Hayakawa, N.Ishibashi
    • Journal Title

      JHEP

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Dynamics of D-branes2004

    • Author(s)
      N.Ishibashi
    • Journal Title

      Suuri-Kagaku 4

      Pages: 23-28

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Loops versus Matrices : The Nonperturbative Aspects of Noncritical String2004

    • Author(s)
      Hanada, Hayakawa, Ishibashi, et al.
    • Journal Title

      Progress of Theoretical Physics 112

      Pages: 131-181

    • NAID

      110001196193

    • Related Report
      2004 Annual Research Report
  • [Journal Article] D-ブレーンの力学2002

    • Author(s)
      石橋 延幸
    • Journal Title

      数理科学 4

      Pages: 23-28

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Perturbative World Volume Dynamics of the Bosonic Membrane and String2001

    • Author(s)
      M.Hayakawa, N.Ishibashi
    • Journal Title

      Nuclear Physics B614

      Pages: 171-194

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Perturbative World Volume Dynamics of the Bosonic Membrane and String2001

    • Author(s)
      M.Hayakawa, N.Ishibashi
    • Journal Title

      Nuclear Physics B 614

      Pages: 171-194

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On the Chemical Potential of c=0 Noncritical String Theory

    • Author(s)
      N.Ishibashi, A.Yamaguchi
    • Journal Title

      JHEP

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On the Chemical Potential of D-instantons in $c=0$ Noncritical String Theory

    • Author(s)
      N.Ishibashi, A.Yamaguchi
    • Journal Title

      JHEP

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Publications] M.Hayakawa, N.Ishibashi: "Perturbative World Volume Dynamics of the Bosonic Membrane and string"Nuclear Physics B. 614. 171-194 (2001)

    • Related Report
      2001 Annual Research Report

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

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