Analysis of infinite dimensional algebras and quantum field theories and application to the mathematical science

• Project/Area Number: 24540210
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: Nagoya University
• Principal Investigator: Awata Hidetoshi 名古屋大学, 多元数理科学研究科, 准教授 (40314059)
• Project Period (FY): 2012-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000); Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: ビラソロ代数 / ディン・庵原・三木代数 / ネクラソフ分配関数 / AGT対応 / ヴィラソロ代数 / AGT予想 / Nekrasov分配関数 / AGT 予想

Outline of Final Research Achievements

We analyzed the representation theory of the q-Virasoro, q-W and Ding-Iohara-Miki algebras. We found that the screening charge is constructed by the product of intertwining operators. By using this we derived Ward-Takahashi identity, loop equation, quantum spectral curve and its regularity. By using the braid and shift relations of the intertwining operators, we obtained R-matrix and (qt)-KZ equation of Ding-Iohara-Miki algebra.

We also analyzed N=6 supersymmetric Chern-Simons-matter theory (ABJ theory). We first calculated the partition function of the lens space matrix model and next obtained the ABJ partition function by analytically continuing it.

Research Products

• [Int'l Joint Research] ITEP/Lebedev Physics Institute(ロシア連邦)
• [Journal Article] Anomaly in RTT relation for DIM algebra and network matrix models (2017)
  • Author(s): Hidetoshi Awata, Hiroaki Kanno, Andrei Mironov, Alexei Morozov, Andrey Morozov, Yusuke Ohkubo and Yegor Zenkevich
  • Journal Title: Nuclear Physics B Volume: 918 Pages: 358-385
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Explicit examples of DIM constraints for network matrix models (2016)
  • Author(s): Hidetoshi Awata, Hiroaki Kanno, Takuya Matsumoto, Andrei Mironov, Alexei Morozov, Andrey Morozov, Yusuke Ohkubo and Yegor Zenkevich,
  • Journal Title: Journal of High Energy Physics Volume: 07 Pages: 1-67
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations (2016)
  • Author(s): Hidetoshi Awata, Hiroaki Kanno, Andrei Mironov, Alexei Morozov, Andrey Morozov, Yusuke Ohkubo and Yegor Zenkevich
  • Journal Title: Journal of High Energy Physics Volume: 10 Pages: 1-49
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Volume Conjecture: Refined and Categorified (2013)
  • Author(s): Hiroyuki Fuji, Sergei Gukov, Piotr Sułkowski, with an appendix by Hidetoshi Awata
  • Journal Title: Adv. Theor. Math. Phys. Volume: 16 Pages: 1669-1777
  • Peer Reviewed
• [Journal Article] Changing the preferred direction of the refined topological vertex (2013)
  • Author(s): Hidetoshi Awata and Hiroaki Kanno
  • Journal Title: Journal of Geometry and Physics Volume: 64 Pages: 91110-91110
  • Peer Reviewed
• [Journal Article] The partition function of ABJ theory (2013)
  • Author(s): Hidetoshi Awata and Shinji Hirano and Masaki Shigemori
  • Journal Title: Progress of Theoretical and Experimental Physics Volume: 053 Issue: 5
  • DOI: 10.1093/ptep/ptt014
  • Peer Reviewed
• [Journal Article] The partition function of ABJ theory (2013)
  • Author(s): Hidetoshi Awata, Shinji Hirano and Masaki Shigemori
  • Journal Title: Progress of Theoretical and Experimental Physics Volume: 053B04
  • Peer Reviewed
• [Journal Article] Localization with a Surface Operator, Irregular Conformal Blocks and Open Topological String (2012)
  • Author(s): Hidetoshi Awata, Hiroyuki Fuji, Hiroaki Kanno, Masahide Manabe and Yasuhiko Yamada
  • Journal Title: Advances in Theoretical and Mathematical Physics Volume: 16
  • Peer Reviewed
• [Presentation] On the Ding-Iohara-Miki algebras (2016)
  • Author(s): Hidetoshi Awata
  • Organizer: Workshop and School "Quantum Geometry, Duality and Matrix Models",August 26--26, 2016
  • Place of Presentation: Lebedev Physics Institute, Moscow, RUSSIA
  • Int'l Joint Research / Invited
• [Presentation] Ding-Iohara 代数のレベル2表現の結晶化 (2015)
  • Author(s): 粟田英資, 大久保勇輔, 藤野弘基
  • Organizer: 日本数学会
  • Place of Presentation: 京都産業大学
  • Year and Date: 2015-09-13
• [Presentation] On Five-dimensional AGT Relations (2014)
  • Author(s): Hidetoshi Awata
  • Organizer: The Simons Center Program ``Gauge Theory, Integrability, and Novel Symmetries of Quantum Field Theory''
  • Place of Presentation: The Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, U.S.A.
  • Year and Date: 2014-09-04
  • Invited
• [Presentation] On AGT conjectures (2013)
  • Author(s): Hidetoshi Awata
  • Organizer: Special lecture in Seoul university
  • Place of Presentation: Physics department, Seoul university, Korea
  • Invited
• [Presentation] Quantum Algebraic Approach to Refined Topological Vertex (2012)
  • Author(s): Hidetoshi Awata
  • Organizer: The XXIX International Colloquium on Group-Theoretical Methods in Physics
  • Place of Presentation: Chern Institute of Mathematics, Tianjin, China
  • Invited