Noncommutative Solitons and application to string theory and integrable systems

• Project/Area Number: 23740182
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Particle/Nuclear/Cosmic ray/Astro physics
• Research Institution: Nagoya University
• Principal Investigator: Hamanaka Masashi 名古屋大学, 多元数理科学研究科, 助教 (70377977)
• Project Period (FY): 2011-04-28 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: ソリトン / インスタントン / 可積分系 / ツイスター理論 / 非可換幾何 / ADHM構成法 / モノポール / ハイパーケーラー計量 / 反自己双対ヤン・ミルズ方程式 / Normal form / Quasideterminant / ハイパーケーラー幾何学

Outline of Final Research Achievements

We have studied solitons in noncommutative spaces. In particular, we have mostly proved a reciprocity in the ADHM construction of noncommutative instantons. Furthermore, by examining algebraic properties of quasideterminants, we clarified
mathematical structure of the noncommutative soliton equations. We also discussed significance of noncommutative extension of them.

Research Products

• [Journal Article] Noncommutative Instantons and Reciprocity (2016)
  • Author(s): Masashi Hamanaka and Toshio Nakatsu
  • Journal Title: 素粒子論研究 電子版 Volume: 23 Pages: 1-4
• [Journal Article] モノポールの数理とD ブレーン (2014)
  • Author(s): 浜中真志
  • Journal Title: 数理科学 Volume: 613 Pages: 45-50
• [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] Noncommutative solitons and quasideterminants (2014)
  • Author(s): Masashi Hamanaka
  • Journal Title: Physica Scripta Volume: 89 Issue: 3 Pages: 38006-38006
  • DOI: 10.1088/0031-8949/89/03/038006
  • Peer Reviewed
• [Journal Article] ソリトン理論・可積分系の非可換空間への拡張 (2014)
  • Author(s): 浜中 真志
  • Journal Title: 素粒子論研究 電子版 Volume: 17 Pages: 1-12
• [Journal Article] 非可換インスタントンのADHM構成法 (2014)
  • Author(s): 浜中 真志, 中津 了勇
  • Journal Title: 九州大学応用力学研究所 研究会報告 Volume: 25AO-S2 Pages: 21-28
  • Peer Reviewed
• [Journal Article] ADHM construction of noncommutative instantons (2013)
  • Author(s): M. Hamanaka and T. Nakatsu
  • Journal Title: arXiv Volume: arXiv:1311.7143 [hep-th] Pages: 1-22
• [Journal Article] Noncommutative ADHM construction revisited (2013)
  • Author(s): Masashi Hamanaka and Toshio Nakatsu
  • Journal Title: International Journal of Modern Physics: Conference Series Volume: 21 Pages: 184-186
  • DOI: 10.1142/s2010194513009720
  • Peer Reviewed
• [Journal Article] Noncommutative instantons revisited (2013)
  • Author(s): Masashi Hamanaka and Toshio Nakatsu
  • Journal Title: Journal of Physics: Conference Series Volume: 411 Pages: 12016-12016
  • DOI: 10.1088/1742-6596/411/1/012016
  • Peer Reviewed
• [Journal Article] Exact construction of noncommutative instantons (2013)
  • Author(s): Masashi Hamanaka and Toshio Nakatsu
  • Journal Title: Frontiers of Mathematics in China Volume: 8 Issue: 5 Pages: 1-16
  • DOI: 10.1007/s11464-013-0281-2
  • Peer Reviewed
• [Journal Article] 非可換インスタントンのADHM構成法 (2012)
  • Author(s): 浜中真志, 中津了勇
  • Journal Title: 素粒子論研究 電子版 Volume: 13 Pages: 1-4
• [Journal Article] Non-commutative Solitons and Quasi-determinants (2012)
  • Author(s): Masashi Hamanaka
  • Journal Title: Proceedings of Symposia in Pure Mathematics Volume: 85 Pages: 381-390
  • Peer Reviewed
• [Journal Article] Hyper-Kahler幾何学の数理と物理 (2012)
  • Author(s): 浜中真志
  • Journal Title: 素粒子論研究 Volume: 119 Pages: 245-279
• [Presentation] Noncommutative Instantons and Reciprocity (2015)
  • Author(s): Masashi Hamanaka and Toshio Nakatsu
  • Organizer: String-Math 2015
  • Place of Presentation: Sanya International Mathematics Forum, Hainan, China
  • Year and Date: 2015-12-31
• [Presentation] Noncommutative Instantons and Reciprocity (2015)
  • Author(s): Masashi Hamanaka and Toshio Nakatsu
  • Organizer: Developments in String Theory and Quantum Field Theory
  • Place of Presentation: Kyoto University, Japan
  • Year and Date: 2015-11-09
• [Presentation] Noncommutative Instantons and Reciprocity (2015)
  • Author(s): Masashi Hamanaka and Toshio Nakatsu
  • Organizer: Geometry in Gauge Theories and String Theory
  • Place of Presentation: KIAS, Korea
  • Year and Date: 2015-09-15
  • Int'l Joint Research
• [Presentation] Yang-Mills Instantons in Noncommutative Spaces (2015)
  • Author(s): Masashi Hamanaka and Toshio Nakatsu
  • Organizer: 60 Years of Yang-Mills Gauge Field Theories
  • Place of Presentation: Nanyang Technological University, Singapore
  • Year and Date: 2015-05-25
  • Int'l Joint Research
• [Presentation] ADHM Construction of Noncommutative Instantons (2015)
  • Author(s): Masashi Hamanaka
  • Organizer: KEK Theory Workshop 2015
  • Place of Presentation: KEK, Japan
  • Year and Date: 2015-01-29
• [Presentation] Noncommutative Solitons and Instantons (2014)
  • Author(s): Masashi Hamanaka
  • Organizer: Strings, Quivers and Cluster Algebras in Mathematical Physics
  • Place of Presentation: KIAS, Korea
  • Year and Date: 2014-12-20
  • Invited
• [Presentation] Noncommutative ADHM Constructions and Duality (2014)
  • Author(s): Masashi Hamanaka
  • Organizer: Search for Classical Analysis and Quantum Integrable Systems
  • Place of Presentation: Kyoto Univeresity, Japan
  • Year and Date: 2014-11-16
  • Invited
• [Presentation] Noncommutative Integrable Systems and Quasideterminants (2014)
  • Author(s): Masashi Hamanaka
  • Organizer: New Trends in Quantum Integrability
  • Place of Presentation: University of Surrey, UK.
  • Year and Date: 2014-08-18 – 2014-08-22
• [Presentation] Noncommutative Instantons and Reciprocity (2014)
  • Author(s): Masashi Hamanaka
  • Organizer: 30th Group Theoretical Methods in Physics
  • Place of Presentation: Ghent, Belgium
  • Year and Date: 2014-07-17
• [Presentation] ADHM construction of Noncommutative Instantons (2013)
  • Author(s): Masashi Hamanaka and Toshio Nakatsu
  • Organizer: Nonlinear Evolution Equations and Wave Phenomena
  • Place of Presentation: ジョージア、米国
  • Invited
• [Presentation] Noncommutative ADHM construction revisited (2012)
  • Author(s): Masashi Hamanaka and Toshio Nakatsu
  • Organizer: Progress in Quantum Field Theory and String Theory
  • Place of Presentation: 大阪市立大学
• [Presentation] Exact construction of noncommutative instantons (2012)
  • Author(s): Masashi Hamanaka and Toshio Nakatsu
  • Organizer: Symmetries and Integrability of Difference Equations
  • Place of Presentation: 寧波、中国
• [Presentation] Noncommutative instantons revisited (2012)
  • Author(s): Masashi Hamanaka and Toshio Nakatsu
  • Organizer: Integrable Systems and Quantum symmetries
  • Place of Presentation: プラハ、チェコ共和国
• [Presentation] ADHM construction of Noncommutative Instantons (2012)
  • Author(s): Masashi Hamanaka and Toshio Nakatsu
  • Organizer: 6th World Congress of Nonlinear Analysts
  • Place of Presentation: アテネ、ギリシャ
  • Invited
• [Presentation] 非可換インスタントンのADHM構成法 (2012)
  • Author(s): 浜中真志, 中津了勇
  • Organizer: 場の理論と弦理論
  • Place of Presentation: 京都大学
• [Presentation] Non-commutative Solitons and Quasi-determinants (2011)
  • Author(s): Masashi Hamanaka
  • Organizer: String-Math 2011
  • Place of Presentation: ペンシルバニア大学
• [Presentation] ソリトン理論・可積分系の非可換空間への拡張
  • Author(s): 浜中 真志
  • Organizer: 京大基研研究会「場の理論と弦理論」
  • Place of Presentation: 京大基研
• [Presentation] 非可換ADHM構成法とインスタントン数の起源
  • Author(s): 浜中 真志, 中津 了勇
  • Organizer: 日本物理学会 素粒子論領域
  • Place of Presentation: 高知大学
• [Presentation] 非可換空間上のインスタントンのADHM構成法
  • Author(s): 浜中 真志, 中津 了勇
  • Organizer: 日本数学会 幾何学分科会
  • Place of Presentation: 愛媛大学
• [Presentation] 非可換インスタントンのADHM構成法
  • Author(s): 浜中 真志, 中津 了勇
  • Organizer: 九大応力研研究会「非線形波動研究の拡がり」
  • Place of Presentation: 九州大学
• [Remarks] アインシュタイン牧場
  • URL: http://www2.yukawa.kyoto-u.ac.jp/~masashi.hamanaka/
• [Remarks] 浜中 真志のホームページ
  • URL: http://www.math.nagoya-u.ac.jp/~hamanaka/hamanaka.html
• [Remarks] アインシュタイン牧場
  • URL: http://www.math.nagoya-u.ac.jp/~hamanaka/ebokujo.html
• [Remarks] アインシュタイン牧場
  • URL: http://www2.yukawa.kyoto-u.ac.jp/~hamanaka/