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M5ブレーン上の6次元(2,0)理論の解析

Research Project

Project/Area Number 14J01791
Research Category

Grant-in-Aid for JSPS Fellows

Allocation TypeSingle-year Grants
Section国内
Research Field Particle/Nuclear/Cosmic ray/Astro physics
Research InstitutionOsaka University

Principal Investigator

森 裕紀  大阪大学, 理学研究科, 特別研究員(DC1)

Project Period (FY) 2014-04-25 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2016: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2015: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2014: ¥1,000,000 (Direct Cost: ¥1,000,000)
KeywordsAdS_7/CFT_6対応 / 非局所演算子 / M弦 / M5ブレーン / Wilsonサーフェス
Outline of Annual Research Achievements

当該年度の研究では、非局所演算子を通じた6次元(2,0)理論の定式化や解析を行った。
超対称性を保つように定義できる非局所演算子の一つがWilsonサーフェス演算子である。6次元(2,0)理論の定式化の一つとして5次元N=2超対称ゲージ理論に等価であるという仮説があり、この下でWilsonサーフェス演算子はWilsonループ演算子として扱うことができる。実は5次元N=2超対称ゲージ理論の分配関数は厳密に計算できChern-Simons行列模型で表現される。これらの事実を用いてWilsonサーフェス演算子の期待値を厳密に計算した。他方、AdS7/CFT6対応というAdS7×S4上のM理論と6次元(2,0)理論が双対な関係にあるという主張がある。この枠組みにおいて、Wilsonサーフェス演算子は泡状幾何とよばれる古典重力解に対応すると考えられてきた。前年度までの研究では、ゲージ群の対称表現と反対称表現に値をもつWilsonサーフェス演算子の期待値を求め、それに双対であると思われていた重力側の解が一致していることを見出した。これはAdS7/CFT6対応を強く支持するとともに、超対称性を保つ範囲で上述の仮説が正しいことを示唆している。本年度ではこの対応関係を一般表現のWilsonサーフェス演算子に拡張することを試みているところである。
他の非局所演算子として余次元2をもつ欠陥演算子があるが、本年度の研究でこの演算子がある場合の分配関数の導出に成功した。6次元(2,0)理論の基本的な物体は粒子ではなくひも状の物体であることが知られている。6次元(2,0)理論のテンソルブランチと呼ばれる領域ではこのひもをM弦と呼ぶ。M弦の分配関数は位相的弦理論の手法によって計算できる。このM弦の観点から余次元2欠陥演算子が挿入された分配関数が系統的に計算できることを示し、演算子としての作用を同定した。

Research Progress Status

28年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

28年度が最終年度であるため、記入しない。

Report

(3 results)
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • 2014 Annual Research Report
  • Research Products

    (26 results)

All 2017 2016 2015 2014 Other

All Int'l Joint Research (1 results) Journal Article (6 results) (of which Peer Reviewed: 6 results,  Open Access: 5 results,  Acknowledgement Compliant: 6 results) Presentation (19 results) (of which Int'l Joint Research: 10 results,  Invited: 1 results)

  • [Int'l Joint Research] National Taiwan University(台湾)

    • Related Report
      2016 Annual Research Report
  • [Journal Article] Surface Operators from M-strings2017

    • Author(s)
      Hironori Mori, Yuji Sugimoto
    • Journal Title

      Physical Review D

      Volume: 95 Issue: 2 Pages: 0260011-15

    • DOI

      10.1103/physrevd.95.026001

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Supersymmetric Rényi Entropy in Two Dimensions2016

    • Author(s)
      Hironori Mori
    • Journal Title

      JHEP

      Volume: 1603 Issue: 3 Pages: 0581-28

    • DOI

      10.1007/jhep03(2016)058

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Varieties of Abelian mirror symmetry on RP^2xS^12016

    • Author(s)
      Hironori Mori, Akinori Tanaka
    • Journal Title

      JHEP

      Volume: 1602 Issue: 2 Pages: 0881-25

    • DOI

      10.1007/jhep02(2016)088

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Abelian 3d mirror symmetry on RP^2xS^1 with N_f = 12015

    • Author(s)
      Akinori Tanaka, Hironori Mori, Takeshi Morita
    • Journal Title

      JHEP

      Volume: 1509 Issue: 9 Pages: 1541-30

    • DOI

      10.1007/jhep09(2015)154

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Superconformal index on RP^2xS^1 and mirror symmetry2015

    • Author(s)
      Akinori Tanaka, Hironori Mori, Takeshi Morita
    • Journal Title

      Physical Review D

      Volume: 91 Issue: 10 Pages: 1050231-24

    • DOI

      10.1103/physrevd.91.105023

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] M5-branes and Wilson Surfaces in AdS_7/CFT_6 Correspondence2014

    • Author(s)
      Hironori Mori, Satoshi Yamaguchi
    • Journal Title

      Physical Review D

      Volume: 90 Issue: 2 Pages: 0260051-11

    • DOI

      10.1103/physrevd.90.026005

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Surface defects from M-strings and open topological string2017

    • Author(s)
      森 裕紀
    • Organizer
      Progress in Quantum Field Theory and String Theory II
    • Place of Presentation
      大阪市立大学 (大阪)
    • Year and Date
      2017-03-27
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Surface operators and M-strings2016

    • Author(s)
      森 裕紀
    • Organizer
      YITP workshop "Strings and Fields 2016"
    • Place of Presentation
      基礎物理学研究所 (京都)
    • Year and Date
      2016-08-08
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Surface operators and M-strings2016

    • Author(s)
      森 裕紀
    • Organizer
      Strings 2016
    • Place of Presentation
      Tsinghua University (中国)
    • Year and Date
      2016-08-01
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 2次元超対称レニーエントロピー2016

    • Author(s)
      森 裕紀
    • Organizer
      日本物理学会第71回年次大会
    • Place of Presentation
      東北学院大学 (仙台)
    • Year and Date
      2016-03-21
    • Related Report
      2015 Annual Research Report
  • [Presentation] 3次元超対称共形指数とミラー対称性2015

    • Author(s)
      森 裕紀
    • Organizer
      第2回日露共同研究国内working seminar「場の量子論と統計力学に於ける行列模型の諸側面」
    • Place of Presentation
      名古屋大学 (名古屋)
    • Year and Date
      2015-12-12
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Superconformal index on RP^2xS^1 and mirror symmetry 22015

    • Author(s)
      森 裕紀
    • Organizer
      KEK Theory Workshop 2015 Dec.
    • Place of Presentation
      KEK (茨城)
    • Year and Date
      2015-12-01
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Surface defects in class S_k2015

    • Author(s)
      森 裕紀
    • Organizer
      8th Taiwan String Workshop
    • Place of Presentation
      National Tsing Hua University (台湾)
    • Year and Date
      2015-11-17
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Surface defects in class S_k and an elliptic algebra2015

    • Author(s)
      森 裕紀
    • Organizer
      YITP workshop "Developments in String Theory and Quantum Field Theory''
    • Place of Presentation
      基礎物理学研究所 (京都)
    • Year and Date
      2015-11-09
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] RP^2xS^1上の3次元N=2ミラー対称性2015

    • Author(s)
      森 裕紀
    • Organizer
      日本物理学会2015年秋季大会
    • Place of Presentation
      大阪市立大学 (大阪)
    • Year and Date
      2015-09-28
    • Related Report
      2015 Annual Research Report
  • [Presentation] クラスS_kにおけるsurface defects2015

    • Author(s)
      森 裕紀
    • Organizer
      日本物理学会2015年秋季大会
    • Place of Presentation
      大阪市立大学 (大阪)
    • Year and Date
      2015-09-28
    • Related Report
      2015 Annual Research Report
  • [Presentation] Abelian 3d mirror symmetry on RP^2xS^12015

    • Author(s)
      森 裕紀
    • Organizer
      KIAS-YITP Joint Workshop 2015: Geometry in Gauge Theories and String Theory
    • Place of Presentation
      KIAS (韓国)
    • Year and Date
      2015-09-15
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Abelian 3d mirror symmetry on RP^2xS^12015

    • Author(s)
      森 裕紀
    • Organizer
      The IX International Symposium on Quantum Theory and Symmetries
    • Place of Presentation
      Ani Plaza Hotel (アルメニア)
    • Year and Date
      2015-07-13
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] M5-branes and Wilson Surfaces in AdS_7/CFT_6 Correspondence2015

    • Author(s)
      森 裕紀
    • Organizer
      Challenges to Quantum Field Theory in Higher Dimensions
    • Place of Presentation
      Technion (イスラエル)
    • Year and Date
      2015-06-29
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Mirror symmetry via RP^2xS^1 index2015

    • Author(s)
      森 裕紀
    • Organizer
      Strings 2015
    • Place of Presentation
      International Centre for Theoretical Sciences/Tata Institute of Fundamental Research (インド)
    • Year and Date
      2015-06-22
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Abelian 3d mirror symmetry on RP^2xS^12015

    • Author(s)
      森 裕紀
    • Organizer
      2nd String Theory in Greater Tokyo
    • Place of Presentation
      理化学研究所 (埼玉)
    • Year and Date
      2015-06-09
    • Related Report
      2015 Annual Research Report
  • [Presentation] M5-branes and Wilson Surfaces in AdS_7/CFT_6 Correspondence2014

    • Author(s)
      Hironori Mori
    • Organizer
      Strings and Fields
    • Place of Presentation
      基礎物理学研究所 (京都)
    • Year and Date
      2014-07-23
    • Related Report
      2014 Annual Research Report
  • [Presentation] M5-branes and Wilson Surfaces in AdS_7/CFT_6 Correspondence2014

    • Author(s)
      Hironori Mori
    • Organizer
      Strings 2014
    • Place of Presentation
      Princeton University (アメリカ)
    • Year and Date
      2014-06-23 – 2014-06-27
    • Related Report
      2014 Annual Research Report
  • [Presentation] M5-branes and Wilson Surfaces in AdS_7/CFT_6 Correspondence2014

    • Author(s)
      Hironori Mori
    • Organizer
      String-Math 2014
    • Place of Presentation
      University of Alberta (カナダ)
    • Year and Date
      2014-06-10
    • Related Report
      2014 Annual Research Report
  • [Presentation] M5-branes and Wilson Surfaces in AdS_7/CFT_6 Correspondence2014

    • Author(s)
      Hironori Mori
    • Organizer
      Holographic vistas on Gravity and Strings
    • Place of Presentation
      基礎物理学研究所 (京都)
    • Year and Date
      2014-05-28
    • Related Report
      2014 Annual Research Report

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Published: 2015-01-22   Modified: 2024-03-26  

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