Gauge theory duality and quiver W-algebras

2019 Fiscal Year Final Research Report

• Project/Area Number: 17K18090
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Particle/Nuclear/Cosmic ray/Astro physics; Mathematical physics/Fundamental condensed matter physics
• Research Institution: Keio University
• Principal Investigator: KIMURA Taro 慶應義塾大学, 自然科学研究教育センター(日吉), 訪問講師 (90760794)
• Project Period (FY): 2017-04-01 – 2020-03-31
• Keywords: ゲージ理論 / 超弦理論 / 共形場理論 / 箙多様体 / BPS/CFT 対応 / 量子可積分系 / 位相的弦理論 / 数理物理

Outline of Final Research Achievements

We have explored the algebraic aspects of the gauge theory, which is one of the universal methodology in theoretical physics. We have obtained the following results: We have established the fractional quiver, which is a new kind of quiver, and clarified the quantum integrability associated with it. We have provided a generic construction of quiver gauge theory with topological string theory based on the algebraic perspective. We have established the supergroup gauge theory. We have established several new mathematical concepts based on the physical insights, and presented these results at the conferences of both physics and mathematics.

Free Research Field

理論物理学

Academic Significance and Societal Importance of the Research Achievements

本研究課題の成果は基礎学問的であり，現段階では社会への直接的な波及効果は未知数である．しかし本研究課題の特徴としてこれらの成果は物理学と数学の境界領域に跨がるものであり，今後より多くの研究分野との関係が明らかになることが期待される．