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Study of D-Branes in Linear Sigma Models

Research Project

Project/Area Number 17K05567
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Mathematical physics/Fundamental condensed matter physics
Research InstitutionThe University of Tokyo

Principal Investigator

Hori Kentaro  東京大学, カブリ数物連携宇宙研究機構, 教授 (30535042)

Project Period (FY) 2017-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords線形シグマ模型 / ゲージ対称性 / 境界上の自由度 / Dブレーン / 次数制限則 / サイバーグ双対性 / 半球面分配関数 / 収束条件 / 積分路の族 / 双対性 / モノドロミー / 強結合相 / カラビ・ヤウ多様体 / ゲージ理論 / 境界自由度 / 境界条件 / テータ角 / スピノル場 / 射影表現 / 平坦中心拡大 / 超弦理論 / 超対称性
Outline of Final Research Achievements

The present research is on the boundary conditions in two dimensional gauge theories formulated on surfaces with boundaries. For a general theory which is not necessarily supersymmetric, we determined the gauge transformation rule of the degrees of freedom on the boundary. For a (2,2) supersymmetric theory, we developed a method to find the grade restriction rule which determines the allowed representations of the gauge group on the boundary. For supersymmetric QCD with orthogonal or symplectic gauge groups, we found that the rule is consistent with Seiberg duality. For gauged linear sigma models, the rule is applied to determine the rule of D-brane transport along paths from one phase to another. The present research introduces an effective method to study D-branes in nongeometric or strongly coupled phases of superstring compactifications.

Academic Significance and Societal Importance of the Research Achievements

量子力学と一般相対論を統一的に含む理論的枠組みの最有力候補が『超弦理論』であるが、その研究において過去30年にわたり中心的役割を果たして来たのが「Dブレーン」である。弦理論を研究する従来の方法は時空の曲率が大きくなるに従い量子補正が増大し破綻してしまう。その問題を解決するのが線形シグマ模型である。本研究では線形シグマ模型におけるDブレーンを調べる有効な方法を開発した。それによりこれまで手の届かなかった領域における超弦理論の基本的な理解が得られるようになった。また、Dブレーンは数学的にも興味深い対象であり、本研究は代数幾何学の新しい予想を生み出している。

Report

(7 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (12 results)

All 2022 2020 2019 2017

All Presentation (12 results) (of which Int'l Joint Research: 12 results,  Invited: 12 results)

  • [Presentation] Grade restriction rule in the Rodland model and its dual2022

    • Author(s)
      Kentaro Hori
    • Organizer
      Geometry of GLSMs
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Introduction to 2d (2,2) supersymmetric gauged linear sigma models2022

    • Author(s)
      Kentaro Hori
    • Organizer
      2D Supersymmetric Theories and Related Topics
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Grade restriction rule and applications2022

    • Author(s)
      Kentaro Hori
    • Organizer
      2D Supersymmetric Theories and Related Topics
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Grade restriction rule and its applications2020

    • Author(s)
      Kentaro Hori
    • Organizer
      GLSMs -- 2020
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Grade Restriction Rule from Hemisphere2019

    • Author(s)
      Kentaro Hori
    • Organizer
      The Geometry and Algebra of Landau-Ginzburg Models
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 3D Mirror Symmetry2019

    • Author(s)
      Kentaro Hori
    • Organizer
      An introductory workshop to 3D mirror symmetry and AGT conjecture
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Mirror Symmetry from 3d to 2d: non-Abelian case2019

    • Author(s)
      Kentaro Hori
    • Organizer
      Workshop on 3d Mirror Symmetry and AGT Conjecture
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Seiberg duality and its consequences2019

    • Author(s)
      Kentaro Hori
    • Organizer
      Geometry and Everything, Fukaya 60
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 2d Seiberg duality, with boundary2017

    • Author(s)
      堀健太朗
    • Organizer
      Flat Connections in Physics and Geometry
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Boundary conditions in 2d (2,2) gauge theories2017

    • Author(s)
      堀健太朗
    • Organizer
      String Math 2017
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Grade restriction rule for QCD with symmetric matters2017

    • Author(s)
      堀健太朗
    • Organizer
      Categorical and Analytic Invariants in Algebraic Geometry V
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Mirror Symmetry - from 3d to 2d2017

    • Author(s)
      堀健太朗
    • Organizer
      Mirror Symmetry and Related Topics 2017
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited

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Published: 2017-04-28   Modified: 2024-01-30  

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