An unexpected symmetry in the integrable structure of gauge and string theories and its root of unity limit

• Project/Area Number: 15K05059
• 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: Osaka City University
• Principal Investigator: Oota Takeshi 大阪市立大学, 大学院理学研究科, 数学研究所専任研究所員 (70419688)
• Co-Investigator(Kenkyū-buntansha): 糸山 浩 大阪市立大学, 大学院理学研究科, 教授 (30243158) ; 吉岡 礼治 大阪市立大学, 大学院理学研究科, 博士研究員 (90514555)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2015: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
• Keywords: 自由場表示 / 変形された量子対称性 / ベキ根極限 / ゲージ理論の可積分構造 / 行列模型 / ループ方程式 / q変形頂点作用素

Outline of Final Research Achievements

The 2d/5d connection is a correspondence between certain two-dimensional field theories and five-dimensional gauge theories with supersymmetry. It implies that the correlation function of the two-dimensional theory and the partition function of the five-dimensional theory are the same. We have determined operators which give a free-field representation of the correlation function and showed that 2d/5d connection holds if the positions of the operators are slightly shifted.
The ``elliptic algebra’’ is a quantum symmetry whose structure constants are expressed in terms of the elliptic functions. We argued that this elliptic algebra plays important roles in the 2d/5d connection.

Research Products

• [Journal Article] Elliptic algebra, Frenkel-Kac construction and root of unity limit (2017)
  • Author(s): Itoyama H、Oota T、Yoshioka R
  • Journal Title: Journal of Physics A: Mathematical and Theoretical Volume: 50 Issue: 36 Pages: 365401-365401
  • DOI: 10.1088/1751-8121/aa8233
  • Peer Reviewed
• [Journal Article] Rainbow tensor model with enhanced symmetry and extreme melonic dominance (2017)
  • Author(s): Itoyama H.、Mironov A.、Morozov A.
  • Journal Title: Physics Letters B Volume: 771 Pages: 180-188
  • DOI: 10.1016/j.physletb.2017.05.043
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Ward identities and combinatorics of rainbow tensor models (2017)
  • Author(s): Itoyama H.、Mironov A.、Morozov A.
  • Journal Title: JHEP Volume: 2017 Issue: 6 Pages: 115-115
  • DOI: 10.1007/jhep06(2017)115
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Cubic constraints for the resolvents of the ABJM matrix model and its cousins (2017)
  • Author(s): Hiroshi Itoyama, Takeshi Oota , Takao Suyama and Reiji Yoshioka
  • Journal Title: International Journal of Modern Physics A Volume: 32 Issue: 11 Pages: 1750056-1750056
  • DOI: 10.1142/s0217751x17500567
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] 行列模型による超対称ゲージ場の理論の量子論の解明と進展 (2016)
  • Author(s): 糸山浩司
  • Journal Title: 日本物理学会誌 Volume: 71 Pages: 607-616
• [Journal Article] The birth of string theory (2016)
  • Author(s): Hiroshi Itoyama
  • Journal Title: Prog. Theor. Exp. Phys. Volume: 2016 (6) Issue: 6 Pages: 06A103-06A103
  • DOI: 10.1093/ptep/ptw063
• [Journal Article] Genus one super-Green function revisited and superstring amplitudes with non-maximal supersymmetry (2016)
  • Author(s): Hiroshi Itoyama and Kohei Yano
  • Journal Title: Progress of Theoretical and Experimental Physics Volume: 2016 (3) Issue: 3 Pages: 033B05-033B05
  • DOI: 10.1093/ptep/ptw019
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Birth of String Theory (2016)
  • Author(s): Hiroshi Itoyama
  • Journal Title: Progress of Theoretical and Experimantal Physics Volume: 2016
• [Journal Article] Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models (2015)
  • Author(s): Hiroshi Itoyama and Reiji Yoshioka
  • Journal Title: Progress of Theoretical and Experimental Physics Volume: 2015 (11) Issue: 11 Pages: 11B103-11B103
  • DOI: 10.1093/ptep/ptv124
  • Peer Reviewed / Open Access
• [Journal Article] Matching branches of a nonperturbative conformal block at its singularity divisor (2015)
  • Author(s): H. Itoyama, A. D. Mironov and A. Yu. Morozov
  • Journal Title: Theoretical and Mathematical Physics Volume: 184 Issue: 1 Pages: 891-923
  • DOI: 10.1007/s11232-015-0305-z
  • Peer Reviewed
• [Presentation] Cut & Join operator ring in Aristotelian tensor model (2018)
  • Author(s): 糸山浩司, A. Mironov, A. Morozov
  • Organizer: 日本物理学会第73回年次大会
• [Presentation] Multi-Penner型行列模型と拡大有効ポテンシャル (2018)
  • Author(s): 矢野勝也, 糸山浩司
  • Organizer: 日本物理学会第73回年次大会
• [Presentation] Elliptic algebra at root of unity limit (2017)
  • Author(s): Takeshi Oota
  • Organizer: 国際会議``Progress in Quantun Field Theory and String Theory II,''
  • Place of Presentation: 大阪市立大学学術情報総合センター10階会議室(大阪府大阪市)
  • Year and Date: 2017-03-28
  • Int'l Joint Research / Invited
• [Presentation] Elliptic algebra at root of unity limit (2017)
  • Author(s): Oota T.
  • Organizer: Workshop and School "Topological Field Theories, String theory and Matrix Models", Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Moscow, Russia
  • Int'l Joint Research / Invited
• [Presentation] Extreme Melonic dominance in rainbow tensor model (2017)
  • Author(s): Itoyama H.
  • Organizer: seminar delivered at Lebedev institute, Moscow, Russia
  • Int'l Joint Research / Invited
• [Presentation] Combinatorial structure of rainbow tensor model (2017)
  • Author(s): Itoyama H.
  • Organizer: workshop “ duality, integrability and matrix model” , Lebedev institute, Moscow, Russia
  • Int'l Joint Research / Invited
• [Presentation] Cut & Join operator ring in Aristotelian tensor model (2017)
  • Author(s): Itoyama H.
  • Organizer: Yukawa institute of theoretical physics
  • Invited
• [Presentation] Cut & Join operator ring in Aristotelian tensor model (2017)
  • Author(s): Itoyama H.
  • Organizer: East Asian symposium on quantum field theory and string theory, KEK
  • Int'l Joint Research / Invited
• [Presentation] Developments of Supersymmetric Gauge Theory by Matrices (2016)
  • Author(s): 糸山浩司
  • Organizer: セミナー
  • Place of Presentation: 量子科学研究所、日本大学理工学部 駿河台校舎4号館(東京都)
  • Year and Date: 2016-11-09
  • Invited
• [Presentation] Cubic Constraints for the Resolvents of the ABJM Matrix Model and Its Cousins (2016)
  • Author(s): Hiroshi Itoyama
  • Organizer: ``Quantum Geometry, Duality and Matrix Models" conference
  • Place of Presentation: Institute for Information Transmission Problems (Kharkevich institute), モスクワ(ロシア)
  • Year and Date: 2016-08-28
  • Int'l Joint Research / Invited
• [Presentation] Loop equations for Chern-Simons-matter matrix models (2016)
  • Author(s): 大田武志
  • Organizer: 理化学研究所ワークショップ「超対称理論の数理的理解の進展」 susyiTHES2016
  • Place of Presentation: 理化学研究所（和光）統合支援施設 二階 大会議室（埼玉県和光市）
  • Year and Date: 2016-08-19
  • Invited
• [Presentation] q-Virasoro/W block at root of unity, parafermions and 2d-4d connection (2016)
  • Author(s): Hiroshi Itoyama
  • Organizer: seminar, physics department, 北京大学
  • Place of Presentation: 北京大学, 北京(中国)
  • Year and Date: 2016-06-01
  • Invited
• [Presentation] The integral representation of solutions of KZ equation and its modification by K operator insertion (2016)
  • Author(s): 吉岡礼治
  • Organizer: 日本物理学会第71回年次大会
  • Place of Presentation: 東北学院大学泉キャンパス(宮城県・仙台市)
  • Year and Date: 2016-03-21
• [Presentation] Integral representation of solutions of KZ equation and a modification (2015)
  • Author(s): Reiji Yoshioka
  • Organizer: ``Quantum Geometry, Duality and Matrix Models'' conference
  • Place of Presentation: Kharkevich Institute, モスクワ, ロシア
  • Year and Date: 2015-08-30
  • Int'l Joint Research / Invited
• [Presentation] q-Virasoro algebra at root of unity and 2d-4d connection (2015)
  • Author(s): Takeshi Oota
  • Organizer: ``Quantum Geometry, Duality and Matrix Models'' conference
  • Place of Presentation: Kharkevich Institute, モスクワ, ロシア
  • Year and Date: 2015-08-29
  • Int'l Joint Research / Invited
• [Book] 波動と場の物理学入門 (2017)
  • Author(s): 糸山 浩司
  • Total Pages: 192
  • Publisher: 京都大学学術出版会
  • ISBN: 9784814001187