M-brain and quantum integrable system

• Project/Area Number: 24540265
• 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: Nagoya University
• Principal Investigator: Kanno Hiroaki 名古屋大学, 多元数理科学研究科, 教授 (90211870)
• Co-Investigator(Renkei-kenkyūsha): AWATA Hidetoshi 名古屋大学, 大学院多元数理科学研究科, 准教授 (40314059) ; MORIYAMA Sanefumi 大阪市立大学, 大学院理学研究科, 准教授 (80402452)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: AGT 関係式 / 超対称ゲージ理論 / ネクラソフ関数 / 行列模型 / ゲージ理論・ベーテ仮説対応 / 超共形指数 / 面作用素 / 面欠陥作用素 / ハイパーケーラー計量 / モノポールウォール / インスタントン分配関数 / Whittaker ベクトル

Outline of Final Research Achievements

We investigated the AGT relation which claims the correspondence between the generating function (Nekrasov partition function) of instanton counting of 4 dimensional gauge theory and the conformal block of 2 dimensional conformal field theory. The AGT relation predicts that we can express the Nekrasov partition function as the inner product of special states on conformal field theory side. We showed how the defining relations of these special states change, when there are matter fields in 4 dimensional SU(3) supersymmetric gauge theory. We also succeeded in describing the defining relations as a result of arising an irregular singularity from the confluence of two regular singularities on the Riemann surface on which conformal filed theory is defined.

Research Products

• [Journal Article] Hyper-Kähler metrics from monopole walls (2014)
  • Author(s): Masashi Hamanaka, Hiroaki Kanno, Daichi Muranaka
  • Journal Title: Physical Review D Volume: 89 Issue: 6 Pages: 65033-65033
  • DOI: 10.1103/physrevd.89.065033
  • Peer Reviewed
• [Journal Article] W_3 irregular states and isolated N=2 superconformal field theories (2013)
  • Author(s): Hiroaki Kanno, Kazunobu Maruvoshi, Shotaro Shiba, Masato
  • Journal Title: JHEP Volume: 1,303 Issue: 3 Pages: 147-147
  • DOI: 10.1007/jhep03(2013)147
  • Peer Reviewed
• [Journal Article] Generalized Whittaker states for instanton counting with fundamental hypermultiplets (2012)
  • Author(s): H. Kanno , M. Taki
  • Journal Title: JHEP Volume: 1205 Issue: 5 Pages: 52-52
  • DOI: 10.1007/jhep05(2012)052
  • Peer Reviewed
• [Presentation] Confluence of regular singularities and the coherent state in quantum field theory (2015)
  • Author(s): Hiroaki Kanno
  • Organizer: 8th International Conference on Science and Mathematics Education for Developing Countries
  • Place of Presentation: University of Yangon, Yangon, Myanmar
  • Year and Date: 2015-12-06
  • Int'l Joint Research / Invited
• [Presentation] Deformed Verlinde algebra and gauge/Bethe correspondence (2015)
  • Author(s): HIroaki Kanno
  • Organizer: Quantum Geometry, Duality and Matrix Models
  • Place of Presentation: Levedev Institute, Moscow, Russia
  • Year and Date: 2015-08-25
• [Presentation] Irregular puncture and isolated N=2 superconformal field theories (2012)
  • Author(s): H. Kanno
  • Organizer: Synthesis of integrabilities in the context of gauge/string duality
  • Place of Presentation: Moscow, Russia
  • Invited
• [Presentation] Irregular puncture and generalized Whittaker state
  • Author(s): 菅野浩明
  • Organizer: 代数幾何学と可積分系におけるモジュライ理論
  • Place of Presentation: 京都大学数理解析研究所
  • Invited
• [Presentation] Superconformal index with surface operator and Macdonald polynomial
  • Author(s): 菅野浩明
  • Organizer: Synthesis of integrabilities in the context of gauge/string duality
  • Place of Presentation: Math. Department of Higher School of Economics, Moscow, Russia
• [Presentation] Irregular puncture and generalized Whittaker state
  • Author(s): 菅野浩明
  • Organizer: International conference on mathematical research, education and application
  • Place of Presentation: the University of Economics and Law, Ho Chi Minh City, Vietnam
  • Invited
• [Presentation] Generalized Whittaker states for instanton counting and the confluence of the punctures
  • Author(s): H. Kanno
  • Organizer: 5th Workshop on Geometric Methods in Theoretical Physics, "Integrability in topological string and field theory"
  • Place of Presentation: Trieste, Italy
  • Invited
• [Presentation] Irregular states and isolated superconformal field theory
  • Author(s): H. Kanno
  • Organizer: 学振２国間交流事業日露共同研究 miniworkshop
  • Place of Presentation: 大阪市