An irregular version of conformal field theory and Painleve equations

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K17560
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Kanazawa University
• Principal Investigator: Nagoya Hajime 金沢大学, 数物科学系, 准教授 (80447367)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: パンルヴェ方程式 / 共形場理論 / モノドロミー保存変形

Outline of Final Research Achievements

In this research project, we studied irregular version of the conformal field theory and Painleve equations. Using representation theory of Virasoro algebra, we defined irregular vertex operators and irregular conformal blocks. Using these irregular conformal blocks, we proved Fourier expansion formulas at infinity of the tau functions of the fourth and fifth Painleve equations and gave conjectural Fourier expansion formulas of the tau functions of the second and third Painleve equations.

Free Research Field

Integrable systems