Derivation of duality and integrability from M-theory

• Project/Area Number: 25400246
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Particle/Nuclear/Cosmic ray/Astro physics
• Research Institution: The 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: ¥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.

Research Products

• [Int'l Joint Research] KIAS(韓国)
• [Int'l Joint Research] 台湾大学(台湾)
• [Int'l Joint Research] ボローニャ大学(イタリア)
• [Int'l Joint Research] 西江大学(韓国)
• [Int'l Joint Research] 国立台湾大学(台湾)
• [Int'l Joint Research] ボローニャ大学(イタリア)
• [Int'l Joint Research] Sogan大学(韓国)
• [Journal Article] (p,q)-webs of DIM representations, 5d N=1 instanton partition functions and qq-characters (2017)
  • 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
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Maulik-Okounkov's R-matrix from Ding-Iohara-Miki algebra (2017)
  • 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
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver (2017)
  • 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
  • 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-Mills (2016)
  • 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
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] The Nambu bracket and M-theory (2016)
  • 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
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Yangian associated with 2D N=1 SCFT (2015)
  • 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
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] SHc realization of minimal model CFT: triality, poset and Burge condition (2015)
  • 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
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Recursive method for the Nekrasov partition function for classical Lie groups (2015)
  • 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
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Construction of Gaiotto states with fundamental multiplets through Degenerate DAHA (2014)
  • 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
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Aspects of Effective Theory for Multiple M5-Branes Compactified On Circle (2014)
  • 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
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] `Partition function of a chiral boson on a 2-torus from the Floreanini-Jackiw Lagrangian (2014)
  • 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
  • Peer Reviewed
• [Journal Article] Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function (2013)
  • 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
  • Peer Reviewed
• [Presentation] Brane web and DIM algebra--Description of duality and qq-character (2017)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Toroidal symmetry and duality in string theory (2017)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Description of (p,q)-brane web from q-deformed toroidal symmetry (2017)
  • Author(s): Yutaka Matsuo
  • Organizer: 25th International Conference on Integrable Systems and Quantum symmetries
  • Int'l Joint Research / Invited
• [Presentation] Quantum toroidal symmetry and SL(2,Z) covariant description of AGT and qq-character (2017)
  • Author(s): Yutaka Matsuo
  • Organizer: INTEGRABILITY IN LOW-DIMENSIONAL QUANTUM SYSTEMS
  • Int'l Joint Research / Invited
• [Presentation] Supersymmetric gauge theories and the duality of q-deformed W($\infty$) algebra (2016)
  • 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
  • Invited
• [Presentation] `Quantum deformation of W($\infty$) and quantum geometry of quiver gauge theories (2016)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] SHc realization of quantum geometry for quiver gauge theories (2016)
  • 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
• [Presentation] Holomorphic field realization of SHc and quantum geometry of quiver gauge theories (2016)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Nambu bracket and M-theory (2015)
  • 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
  • Invited
• [Presentation] SHc and W-algebras; level-rank duality, minimal models and poset (2015)
  • 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
  • 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
  • Invited
• [Presentation] An integrable lattice hierarchy associated with N=2 gauge theories (2014)
  • 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
  • Invited
• [Presentation] Instanton partition function, DDAHA and recursion formula (2014)
  • Author(s): Yutaka Matsuo
  • Organizer: JSPS/RFBR collaboration
  • Place of Presentation: KKR琵琶湖（大津市・滋賀県）
  • Invited
• [Presentation] Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function (2013)
  • Author(s): Yutaka Matsuo
  • Organizer: PASCOS
  • Place of Presentation: 台湾大学（台北市・台湾）
  • Invited
• [Presentation] Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function (2013)
  • Author(s): Yutaka Matsuo
  • Organizer: CFT and integrability
  • Place of Presentation: Sogan大学（ソウル・大韓民国）
  • Invited
• [Presentation] Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function (2013)
  • 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）
  • Invited
• [Remarks]
  • URL: http://www-hep.phys.s.u-tokyo.ac.jp/~matsuo/