Realization of lattice Leibniz rule and construction of supersymmetry on lattice

• Project/Area Number: 25400260
• 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: Ehime University
• Principal Investigator: So Hiroto 愛媛大学, 理工学研究科(理学系), 教授 (20196992)
• Co-Investigator(Kenkyū-buntansha): 坂本 眞人 神戸大学, 理学研究科, 准教授 (30183817) ; 加藤 光裕 東京大学, 大学院総合文化研究科, 教授 (80185876)
• Project Period (FY): 2013-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 超対称性 / 場の理論 / 格子場の理論 / 量子力学 / 国内共同研究 / 格子超対称性 / ライプニッツ則

Outline of Final Research Achievements

We propose a new type field product based on cyclic Leibniz rule which is characteristic in lattice theory. Using the product, we formulated real and complex supersymmetric quantum mechanics on lattice. Still in the real model the Witten index has been calculated by localization technique. For complex model, We have prove a non-renormalization theorem on a kind of F-term keeping finite lattice constant.

Research Products

• [Journal Article] Non-renormalization theorem in a lattice supersymmetric theory and the cyclic Leibniz rule (2017)
  • Author(s): Kato Mitsuhiro、Sakamoto Makoto、So Hiroto
  • Journal Title: Progress of Theoretical and Experimental Physics Volume: 2017 Issue: 4 Pages: 1-31
  • DOI: 10.1093/ptep/ptx045
  • NAID: 120006352318
  • Peer Reviewed / Open Access
• [Journal Article] A criterion for lattice supersymmetry: cyclic Leibniz rule (2013)
  • Author(s): Mitsuhiro Kato, Makoto Sakamoto, Hiroto So
  • Journal Title: Journal of High Energy Physics Volume: Vol.1305、No.5 Issue: 5 Pages: 89-89
  • DOI: 10.1007/jhep05(2013)089
  • NAID: 120005468176
  • Peer Reviewed
• [Journal Article] Cyclic Leibniz rule: a formulation of supersymmetry on lattice (2013)
  • Author(s): M. Kato, M. Sakamoto and H.So
  • Journal Title: Proceedings of Science Volume: Lattice2013 Pages: 356-356
• [Presentation] Cyclic Leibniz Rule, Cohomology and Non-renormalization Theorem in Lattice Supersymmetry (2016)
  • Author(s): Mitsuhiro Kato, Makoto Sakamoto and Hiroto So
  • Organizer: The 24th International Conference on Supersymmetry and Unification of Fundamental Interactions(SUSY21016)
  • Place of Presentation: The University of Melbourne, Australia
  • Year and Date: 2016-07-04
  • Int'l Joint Research
• [Presentation] Cohomological property of CLR-realized supersymmetric quantum mechanics on lattice (2016)
  • Author(s): 宗 博人(口頭発表)、坂本眞人、加藤光裕
  • Organizer: 日本物理学会第71回年次大会
  • Place of Presentation: 東北学院大学、宮城県・仙台市
  • Year and Date: 2016-03-22
• [Presentation] 格子超対称性における非繰り込み定理と巡回ライプニッツ則 (2014)
  • Author(s): 加藤 光裕
  • Organizer: 日本物理学会2014年秋季大会
  • Place of Presentation: 佐賀大学(佐賀県・佐賀市)
  • Year and Date: 2014-09-19
• [Presentation] Non-renormalization theorem and cyclic Leibniz rule in lattice supersymmetry (2014)
  • Author(s): Makoto Sakamoto
  • Organizer: The 32nd International Symposium on Lattice Field Theory
  • Place of Presentation: Columbia University(NewYork City,USA)
  • Year and Date: 2014-06-27
• [Presentation] Cyclic Leibniz rule: a formulation of supersymmetry on lattice (2013)
  • Author(s): 宗 博人
  • Organizer: 31st International Symposium on Lattice Field Theory
  • Place of Presentation: ドイツ連邦共和国、マインツ
• [Presentation] A supersymmetric complex quantum mechanical model on lattice and advantages of cyclic Leibniz rule (2013)
  • Author(s): 坂本 眞人
  • Organizer: 日本物理学会2013年秋季大会
  • Place of Presentation: 高知大学