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Derivation of duality and integrability from M-theory

Research Project

Project/Area Number 25400246
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Particle/Nuclear/Cosmic ray/Astro physics
Research InstitutionThe University of Tokyo

Principal Investigator

Matsuo Yutaka  東京大学, 大学院理学系研究科(理学部), 准教授 (50202320)

Project Period (FY) 2013-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywordsストリング理論 / ゲージ理論 / 双対性 / 可解模型 / 量子変形 / Gerbe / 表現論 / 超対称性 / 量子代数 / M理論 / ブレーン / インスタントン / q変形代数 / 無限次元対称性 / Seiberg-Witten曲線 / Virasoro代数 / 可解格子模型 / Seiberg-Witten理論 / M理論 / 非線形代数 / ソリトン / 超対称ゲージ理論 / 自己双対場 / 戸田方程式 / W代数
Outline of Final Research Achievements

Sometimes, one physical system has some apparently different descriptions. Such property is referred to as duality. While it is beneficial to extend the methods to study the system, it is hard to derive it rigorously. In this study, I explore the duality in the gauge theory which is essential to describe the elemental particle physics. I found that a q-deformed infinite dimensional symmetry plays a unique role to explain it and explored its properties. Also, I developed a geometrical method to define the duality in M-theory.

Report

(6 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (36 results)

All 2017 2016 2015 2014 2013 Other

All Int'l Joint Research (7 results) Journal Article (12 results) (of which Int'l Joint Research: 5 results,  Peer Reviewed: 12 results,  Open Access: 6 results,  Acknowledgement Compliant: 7 results) Presentation (16 results) (of which Int'l Joint Research: 7 results,  Invited: 15 results) Remarks (1 results)

  • [Int'l Joint Research] KIAS(韓国)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] 台湾大学(台湾)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] ボローニャ大学(イタリア)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] 西江大学(韓国)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] 国立台湾大学(台湾)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] ボローニャ大学(イタリア)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] Sogan大学(韓国)

    • Related Report
      2015 Research-status Report
  • [Journal Article] (p,q)-webs of DIM representations, 5d N=1 instanton partition functions and qq-characters2017

    • Author(s)
      Jean-Emile Bourgine, Masayuki Fukuda, Koichi Harada, Yutaka Matsuo, Rui-Dong Zhu
    • Journal Title

      Journal of High Energy Physics

      Volume: 11, 034 Issue: 11 Pages: 1-42

    • DOI

      10.1007/jhep11(2017)034

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Maulik-Okounkov's R-matrix from Ding-Iohara-Miki algebra2017

    • Author(s)
      Masayuki Fukuda, Koichi Harada, Yutaka Matsuo, Rui-Dong Zhu
    • Journal Title

      Progress of Theoretical and Experimental Physics

      Volume: no. 9, 093A01 Issue: 9 Pages: 1-19

    • DOI

      10.1093/ptep/ptx123

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver2017

    • Author(s)
      Jean-Emile Bourgine, Masayuki Fukuda, Yutaka Matsuo, Rui-Dong Zhu
    • Journal Title

      Journal of High Energy Physics

      Volume: 12, 015 Issue: 12 Pages: 1-27

    • DOI

      10.1007/jhep12(2017)015

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Coherent states in quantum W_{1+\infty} algebra and qq-character for 5d Super Yang-Mills2016

    • Author(s)
      Jean-Emile Bourgine, Masayuki Fukuda, Yutaka Matsuo, Hong Zhang, Rui-Dong Zhu
    • Journal Title

      Progress of Theoretical and Experimental Physics

      Volume: no.12, 123B05 Issue: 12 Pages: 1-41

    • DOI

      10.1093/ptep/ptw165

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] The Nambu bracket and M-theory2016

    • Author(s)
      Pei-Ming Ho, Yutaka Matsuo
    • Journal Title

      Progress of Theoretical and Experimental Physics

      Volume: 2016 Issue: 6 Pages: 06A104-06A104

    • DOI

      10.1093/ptep/ptw075

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Yangian associated with 2D N=1 SCFT2015

    • Author(s)
      Rui-Dong Zhu, Yutaka Matsuo
    • Journal Title

      Progress of Theoretical and Experimental Physics

      Volume: 9 Issue: 9 Pages: 093A01-093A01

    • DOI

      10.1093/ptep/ptv116

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] SHc realization of minimal model CFT: triality, poset and Burge condition2015

    • Author(s)
      M. Fukuda, S. Nakamura, Y. Matsuo, Rui-Dong Zhu
    • Journal Title

      Journal of high energy physics

      Volume: 1511 Issue: 11 Pages: 168-168

    • DOI

      10.1007/jhep11(2015)168

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Recursive method for the Nekrasov partition function for classical Lie groups2015

    • Author(s)
      Satoshi Nakamura, Futoshi Okazawa, Yutaka Matsuo
    • Journal Title

      Progress of Theoretical and Experimental Physics

      Volume: 3 Issue: 3

    • DOI

      10.1093/ptep/ptv014

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Construction of Gaiotto states with fundamental multiplets through Degenerate DAHA2014

    • Author(s)
      Yutaka Matsuo, Chaiho Rim, Hong Zhang
    • Journal Title

      Journal of High Energy Physics

      Volume: 1409 Issue: 9 Pages: 028-028

    • DOI

      10.1007/jhep09(2014)028

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Aspects of Effective Theory for Multiple M5-Branes Compactified On Circle2014

    • Author(s)
      Pei-Ming Ho, Yutaka Matsuo
    • Journal Title

      Journal of High Energy Physics

      Volume: 1412 Issue: 12 Pages: 154-154

    • DOI

      10.1007/jhep12(2014)154

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] `Partition function of a chiral boson on a 2-torus from the Floreanini-Jackiw Lagrangian2014

    • Author(s)
      W.-M.Chen, P.-M.Ho, H.-c.Kao, F.S.Khoo and Y.Matsuo
    • Journal Title

      PTEP

      Volume: 3 Issue: 3 Pages: 33B02-0

    • DOI

      10.1093/ptep/ptu021

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function2013

    • Author(s)
      Shoichi Kanno, Yutaka Matsuo, Hong Zhang
    • Journal Title

      Journal of High Energy Physics

      Volume: 1308 Issue: 8 Pages: 28-28

    • DOI

      10.1007/jhep08(2013)028

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] Brane web and DIM algebra--Description of duality and qq-character2017

    • Author(s)
      松尾 泰
    • Organizer
      Progress in Quantum Field Theory and String Theory II
    • Place of Presentation
      大阪市立大学 (大阪府 住吉区)
    • Year and Date
      2017-03-27
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Toroidal symmetry and duality in string theory2017

    • Author(s)
      松尾 泰
    • Organizer
      String and M-theory in Okinawa
    • Place of Presentation
      OIST (沖縄県 国頭郡)
    • Year and Date
      2017-03-06
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Description of (p,q)-brane web from q-deformed toroidal symmetry2017

    • Author(s)
      Yutaka Matsuo
    • Organizer
      25th International Conference on Integrable Systems and Quantum symmetries
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Quantum toroidal symmetry and SL(2,Z) covariant description of AGT and qq-character2017

    • Author(s)
      Yutaka Matsuo
    • Organizer
      INTEGRABILITY IN LOW-DIMENSIONAL QUANTUM SYSTEMS
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Supersymmetric gauge theories and the duality of q-deformed W($\infty$) algebra2016

    • Author(s)
      松尾 泰
    • Organizer
      AGTの物理と数学
    • Place of Presentation
      中央大学 (東京都 文京区)
    • Year and Date
      2016-10-28
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] `Quantum deformation of W($\infty$) and quantum geometry of quiver gauge theories2016

    • Author(s)
      松尾 泰
    • Organizer
      `Classical and quantum integrable systems and supersymmetry
    • Place of Presentation
      南開大学(天津市 中国)
    • Year and Date
      2016-09-19
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] SHc realization of quantum geometry for quiver gauge theories2016

    • Author(s)
      松尾 泰
    • Organizer
      日本物理学会
    • Place of Presentation
      東北学院大学 (宮城県・仙台市)
    • Year and Date
      2016-03-19
    • Related Report
      2015 Research-status Report
  • [Presentation] Holomorphic field realization of SHc and quantum geometry of quiver gauge theories2016

    • Author(s)
      Yutaka Matsuo
    • Organizer
      Higher Structures in String Theory and M-theory
    • Place of Presentation
      東北大学 (宮城県・仙台市)
    • Year and Date
      2016-03-07
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Nambu bracket and M-theory2015

    • Author(s)
      松尾 泰
    • Organizer
      南部陽一郎追悼講演会
    • Place of Presentation
      大阪市立大学 (大阪府・大阪市)
    • Year and Date
      2015-09-29
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] SHc and W-algebras; level-rank duality, minimal models and poset2015

    • Author(s)
      Yutaka Matsuo
    • Organizer
      Quantum geometry, Duality and Matrix models
    • Place of Presentation
      モスクワ (ロシア)
    • Year and Date
      2015-08-24
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] W代数と可解格子模型--Maulick-Okounkovのアプローチとその発展2015

    • Author(s)
      松尾 泰
    • Organizer
      数学・物理における可積分性の諸相
    • Place of Presentation
      大阪市立大学・大阪府
    • Year and Date
      2015-03-09 – 2015-03-11
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] An integrable lattice hierarchy associated with N=2 gauge theories2014

    • Author(s)
      松尾 泰
    • Organizer
      静岡素粒子集中セミナー
    • Place of Presentation
      静岡大学・静岡県
    • Year and Date
      2014-12-04 – 2014-12-06
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Instanton partition function, DDAHA and recursion formula2014

    • Author(s)
      Yutaka Matsuo
    • Organizer
      JSPS/RFBR collaboration
    • Place of Presentation
      KKR琵琶湖(大津市・滋賀県)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function2013

    • Author(s)
      Yutaka Matsuo
    • Organizer
      PASCOS
    • Place of Presentation
      台湾大学(台北市・台湾)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function2013

    • Author(s)
      Yutaka Matsuo
    • Organizer
      CFT and integrability
    • Place of Presentation
      Sogan大学(ソウル・大韓民国)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function2013

    • Author(s)
      Yutaka Matsuo
    • Organizer
      Workshop `New Topics on Stochastic and Quantum Interacting Particle Systems'
    • Place of Presentation
      東京大学(東京都)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Remarks]

    • URL

      http://www-hep.phys.s.u-tokyo.ac.jp/~matsuo/

    • Related Report
      2017 Annual Research Report

URL: 

Published: 2014-07-25   Modified: 2022-08-18  

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