Deformation quantizations for instantons and related noncommutative deformations of topological invariants

2015 Fiscal Year Final Research Report

• Project/Area Number: 23540117
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Tokyo University of Science (2013-2015); Kushiro National College of Technology (2011-2012)
• Principal Investigator: Sako Akifumi 東京理科大学, 理学部, 准教授 (00424200)
• Co-Investigator(Kenkyū-buntansha): MAEDA Yoshiaki 東北大学, 知の創出センター, 教授 (40101076)
• Project Period (FY): 2011-04-28 – 2016-03-31
• Keywords: 非可換幾何 / 変形量子化 / ゲージ理論 / BPS方程式 / インスタントン

Outline of Final Research Achievements

Gauge theories on noncommutative homogeneous Kahler manifolds have been studied. To make the noncommutative manifolds, we used the deformation quantization with separation of variables for Kahler manifolds which was given by Karabegov. We constructed models of noncommutative gauge theories that are connected with usual Yang-Mills theories in the commutative limits. As examples, we gave noncommutative CP^N and noncommutative CH^N at first and construct gauge theories on them. In order to make theories as non-formal power series, the Fock representations of the noncommutative manifolds were constructed, too. Using the representations, the Euler-Lagrange equations and the BPS equations (including an instanton type equation) of the gauge theories were derived, and nontrivial solutions were also obtained.

Free Research Field

微分幾何