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Duality and algebra of loop operators in supersymmetric field theories: integrable systems and cluster algebras

Research Project

Project/Area Number 15K17634
Research Category

Grant-in-Aid for Young Scientists (B)

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

Principal Investigator

Yamazaki Masahito  東京大学, カブリ数物連携宇宙研究機構, 准教授 (00726599)

Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords量子場の理論 / 可積分系 / クラスター代数 / 超弦理論 / 超対称場の理論 / 共形場理論
Outline of Final Research Achievements

(1) constructed new integrable models from 2d quantum field theory (2) comprehensive discussion of topological defects in 3d/3d correspondence, by cluster algebra, AdS/CFT correspondence etc. (3) proposed a novel generalization of the Yang-Baxter equation, based on cluster algebras (4) proposed a new all-order conjecture for the closed 3-manifold version of the volume conjecture (5) formulated quantum discrete Today theory via cluster algebras, and discussed connection with quantum chaos (6) discussed semi-classical limit of the integrable models arising from supersymmetric gauge theories, and showed that we obtain chiral Potts and other discrete classical integrable models

Report

(4 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (40 results)

All 2018 2017 2016 2015 Other

All Int'l Joint Research (4 results) Journal Article (18 results) (of which Int'l Joint Research: 17 results,  Peer Reviewed: 18 results,  Open Access: 6 results,  Acknowledgement Compliant: 8 results) Presentation (15 results) (of which Int'l Joint Research: 15 results,  Invited: 15 results) Book (1 results) Remarks (2 results)

  • [Int'l Joint Research] プリンストン高等研究所/ラトガース大学/カリフォルニア大学バークリー校(米国)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] ウプサラ大学(スウェーデン)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] ペリメーター研究所(カナダ)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] ソウル国立大学(韓国)

    • Related Report
      2017 Annual Research Report
  • [Journal Article] Tensor modes in pure natural inflation2018

    • Author(s)
      Nomura Yasunori、Yamazaki Masahito
    • Journal Title

      Physics Letters B

      Volume: 780 Pages: 106-110

    • DOI

      10.1016/j.physletb.2018.02.071

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Lens elliptic gamma function solution of the Yang?Baxter equation at roots of unity2018

    • Author(s)
      Kels Andrew P、Yamazaki Masahito
    • Journal Title

      Journal of Statistical Mechanics: Theory and Experiment

      Volume: 2018 Issue: 2 Pages: 023108-023108

    • DOI

      10.1088/1742-5468/aaa8fd

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Pure natural inflation2018

    • Author(s)
      Nomura Yasunori、Watari Taizan、Yamazaki Masahito
    • Journal Title

      Physics Letters B

      Volume: 776 Pages: 227-230

    • DOI

      10.1016/j.physletb.2017.11.052

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] All-Order Volume Conjecture for Closed 3-Manifolds from Complex Chern?Simons Theory2018

    • Author(s)
      Gang Dongmin、Romo Mauricio、Yamazaki Masahito
    • Journal Title

      Communications in Mathematical Physics

      Volume: 359 Issue: 3 Pages: 915-936

    • DOI

      10.1007/s00220-018-3115-y

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Comments on Exchange Graphs in Cluster Algebras2018

    • Author(s)
      Kim Hyun Kyu、Yamazaki Masahito
    • Journal Title

      Experimental Mathematics

      Volume: 0 Issue: 1 Pages: 1-22

    • DOI

      10.1080/10586458.2018.1437849

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Quantum trilogy: discrete Toda, Y-system and chaos2018

    • Author(s)
      Yamazaki Masahito
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 51 Issue: 5 Pages: 053002-053002

    • DOI

      10.1088/1751-8121/aaa08e

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Determinant formula for parabolic Verma modules of Lie superalgebras2018

    • Author(s)
      Yoshiki Oshima, Masahito Yamazaki
    • Journal Title

      Journal of Algebra

      Volume: 495 Pages: 51-80

    • DOI

      10.1016/j.jalgebra.2017.11.011

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] From 4d Yang-Mills to 2d CP^{N-1} model: IR problem and confinement at weak coupling2017

    • Author(s)
      Masahito Yamazaki, Kazuya Yonekura
    • Journal Title

      Journal of High Energy Physics

      Volume: JHEP07(2017)088 Issue: 7 Pages: 88-88

    • DOI

      10.1007/jhep07(2017)088

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] BPS graphs: from spectral networks to BPS quivers2017

    • Author(s)
      Gabella Maxime、Longhi Pietro、Park Chan Y.、Yamazaki Masahito
    • Journal Title

      Journal of High Energy Physics

      Volume: 2017 Issue: 7 Pages: 32-32

    • DOI

      10.1007/jhep07(2017)032

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Cluster-enriched Yang?Baxter equation from SUSY gauge theories2017

    • Author(s)
      Yamazaki Masahito
    • Journal Title

      Letters in Mathematical Physics

      Volume: TBD

    • DOI

      10.1007/s11005-017-1038-8

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Taming Supersymmetric Defects in 3d-3d Correspondence2016

    • Author(s)
      Donmin gang, Nakwoo Kim, Mauricio Romo, Masahito Yamazaki
    • Journal Title

      Journal of Physics A

      Volume: 49 Issue: 30 Pages: 30LT02-30LT02

    • DOI

      10.1088/1751-8113/49/30/30lt02

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Aspects of defects in 3d-3d correspondence2016

    • Author(s)
      Donmin gang, Nakwoo Kim, Mauricio Romo, Masahito Yamazaki
    • Journal Title

      JHEP

      Volume: 1610 Issue: 10 Pages: 062-062

    • DOI

      10.1007/jhep10(2016)062

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] gauging and decoupling in 3d N=2 theories2016

    • Author(s)
      Jeongseog Lee, Masahito Yamazaki
    • Journal Title

      JHEP

      Volume: 1606 Issue: 10 Pages: 077-077

    • DOI

      10.1007/jhep10(2016)035

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] spectral sum rules for confining large-N theories2016

    • Author(s)
      Aleksey Cherman, David McGady, Masahito Yamazaki
    • Journal Title

      JHEP

      Volume: 1606 Issue: 6 Pages: 095-095

    • DOI

      10.1007/jhep06(2016)095

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] recursion relation for conformal blocks2016

    • Author(s)
      Joao Penedones, Emlio Trevisani, Masahito Yamazaki
    • Journal Title

      JHEP

      Volume: 1609 Issue: 9 Pages: 070-070

    • DOI

      10.1007/jhep09(2016)070

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Quantum Dilogarithm Identities at Root of Unity2016

    • Author(s)
      Ivan Chi-Ho Ip and Masahito Yamazaki
    • Journal Title

      Int. Math. Res. Not. 2016, 669-695 (2016)

      Volume: 2016 Issue: 3 Pages: 669-695

    • DOI

      10.1093/imrn/rnv141

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Integrability from 2d N=(2,2) Dualities"2015

    • Author(s)
      Masahito Yamazaki and Wenbin Yan
    • Journal Title

      J. Phys. A 48, 394001 (2015)

      Volume: 48 Issue: 39 Pages: 394001-394001

    • DOI

      10.1088/1751-8113/48/39/394001

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Casimir energy of confining large N gauge theories2015

    • Author(s)
      Gokce Basar, Aleksey Cherman, David A. McGady and Masahito Yamazaki
    • Journal Title

      Phys. Rev. Lett. 114, 251604 (2015)

      Volume: 114 Issue: 25 Pages: 251604-251604

    • DOI

      10.1103/physrevlett.114.251604

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] Polology of Superconformal Blocks2018

    • Author(s)
      Masahito Yamazaki
    • Organizer
      Symposium: Bootstrap Approach to Conformal Field Theories and Applications
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Gauge Theory and Integrability2018

    • Author(s)
      Masahito Yamazaki
    • Organizer
      Rikkyo MathPhys 2018
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] All-order volume conjecture for closed 3-manifolds2018

    • Author(s)
      Masahito Yamazaki
    • Organizer
      Quantum Knot Homology and Supersymmetric Gauge Theories
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Pure Natural Inflation2018

    • Author(s)
      Masahito Yamazaki
    • Organizer
      Pacific 2018
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] From 4d Yang-Mills to 2d CP^{N-1} model2017

    • Author(s)
      Masahito Yamazaki
    • Organizer
      Resurgent Asymptotics in Physics and Mathematics
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Stokes Graphs, Quivers and BPS Graphs2017

    • Author(s)
      Masahito Yamazaki
    • Organizer
      Resurgence in Gauge and String Theory
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Integrability lattice models from four-dimensional gauge theory2017

    • Author(s)
      Masahito Yamazaki
    • Organizer
      Tokyo-Berkeley Summer School "Geometry, representation theory and mathematical physics"
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Integrable Lattice Models from Gauge Theory2017

    • Author(s)
      Masahito Yamazaki
    • Organizer
      workshop on quantum fields, knots and integrable systems
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Spectral Networks and BPS Quivers2016

    • Author(s)
      Masahito Yamazaki
    • Organizer
      resurgence at Kavli IPMU
    • Place of Presentation
      Kavli IPMU, Chiba, Kashiwa
    • Year and Date
      2016-12-15
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Integrability from Four-Dimensional Gauge Theory2016

    • Author(s)
      Masahito Yamazaki
    • Organizer
      Workshop on Geometric correspondence of Gauge Theories
    • Place of Presentation
      SISSA,Trieste,Italy
    • Year and Date
      2016-09-14
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] mirror symmetry and quivers2016

    • Author(s)
      Masahito Yamazaki
    • Organizer
      FRG workshop "Special Holonomy Geometry, Mirror, and Supersymmetry”, Harvard university
    • Place of Presentation
      Harvard University,Cambridge,USA
    • Year and Date
      2016-05-10
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] QFT4.02016

    • Author(s)
      Masahito Yamazaki
    • Organizer
      PCTS celebration
    • Place of Presentation
      Princeton Center for Theoretical Science,Princeton University, Princeton, USA
    • Year and Date
      2016-05-06
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Knots in 3d-3d Correspondence2015

    • Author(s)
      Masahito Yamazaki
    • Organizer
      Master Lectures on Mathematical Physics: Edward Witten",
    • Place of Presentation
      Sanya, China
    • Year and Date
      2015-12-28
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Dilogarithm Identities and Cluster Algebras2015

    • Author(s)
      Masahito Yamazaki
    • Organizer
      Tokyo-Berkeley Summer School "Geometry and Mathematical Physics
    • Place of Presentation
      Kashiwa, Japan
    • Year and Date
      2015-07-31
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Yang-Baxter Duality2015

    • Author(s)
      Masahito Yamazaki
    • Organizer
      Baxter 2015: Exactly Solved Models & Beyond
    • Place of Presentation
      Palm Cove, australia
    • Year and Date
      2015-07-02
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Book] 場の理論の構造と幾何2015

    • Author(s)
      山崎雅人
    • Total Pages
      232
    • Publisher
      サイエンス社
    • Related Report
      2015 Research-status Report
  • [Remarks] Masahito Yamazaki's personal web site

    • URL

      http://member.ipmu.jp/masahito.yamazaki/publications.shtml

    • Related Report
      2017 Annual Research Report
  • [Remarks] Masahito Yamazaki's personal web site

    • URL

      http://member.ipmu.jp/masahito.yamazaki/

    • Related Report
      2015 Research-status Report

URL: 

Published: 2015-04-16   Modified: 2022-06-07  

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