Study of Argyles-Douglas theory based on quantum integrability

2022 Fiscal Year Final Research Report

• Project/Area Number: 18K03643
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 15010:Theoretical studies related to particle-, nuclear-, cosmic ray and astro-physics
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: Ito Katsushi 東京工業大学, 理学院, 教授 (60221769)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Keywords: 超対称性 / 量子可積分模型 / ODE/IM対応 / Argyres-Douglas理論 / Seiberg-Witten理論

Outline of Final Research Achievements

Four-dimensional N=2 superconformal field theories called the Argyres-Douglas theories are non-local theories, where we cannot apply standard method of field theories. In this study, we focus on the quantum Seiberg-Witten periods which characterize the low-energy effective theories and studied them using the exact WKB analysis and the ODE/IM correspondence. I determined the quantum Seiberg-WItten periods for the Schroedinger-type differential equations with a polynomial potential by the thermodynamic Bethe ansatz(TBA) equations. By generalizing the ODE/IM correspondence to the higher-order ODE, we also confirm the relation between the quantum Seiberg-Witten periods and the TBA equations.

Free Research Field

素粒子論

Academic Significance and Societal Importance of the Research Achievements

摂動論など従来の手法で解析が困難と見られてきた強結合領域における場の量子論を, 2次元の量子可積分模型や常微分方程式の解の接続問題と共通な数学的構造があることを見出すことにより研究する新しい手法を開発した。またこの手法は量子力学のスペクトル問題を量子可積分的手法により厳密に解く新しい手法を与えるなど、摂動論を越えた物理の理解に大きく貢献するものである。