Analysis of infinite dimensional algebras and quantum field theories and application to the mathematical science

2016 Fiscal Year Final Research Report

• Project/Area Number: 24540210
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: Nagoya University
• Principal Investigator: Awata Hidetoshi 名古屋大学, 多元数理科学研究科, 准教授 (40314059)
• Project Period (FY): 2012-04-01 – 2017-03-31
• Keywords: ビラソロ代数 / ディン・庵原・三木代数 / ネクラソフ分配関数 / AGT対応

Outline of Final Research Achievements

We analyzed the representation theory of the q-Virasoro, q-W and Ding-Iohara-Miki algebras. We found that the screening charge is constructed by the product of intertwining operators. By using this we derived Ward-Takahashi identity, loop equation, quantum spectral curve and its regularity. By using the braid and shift relations of the intertwining operators, we obtained R-matrix and (qt)-KZ equation of Ding-Iohara-Miki algebra.

We also analyzed N=6 supersymmetric Chern-Simons-matter theory (ABJ theory). We first calculated the partition function of the lens space matrix model and next obtained the ABJ partition function by analytically continuing it.

Free Research Field

無限可積分系