M-brain and quantum integrable system

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540265
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Particle/Nuclear/Cosmic ray/Astro physics
• Research Institution: Nagoya University
• Principal Investigator: Kanno Hiroaki 名古屋大学, 多元数理科学研究科, 教授 (90211870)
• Co-Investigator(Renkei-kenkyūsha): AWATA Hidetoshi 名古屋大学, 大学院多元数理科学研究科, 准教授 (40314059) ; MORIYAMA Sanefumi 大阪市立大学, 大学院理学研究科, 准教授 (80402452)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: AGT 関係式 / 超対称ゲージ理論 / ネクラソフ関数

Outline of Final Research Achievements

We investigated the AGT relation which claims the correspondence between the generating function (Nekrasov partition function) of instanton counting of 4 dimensional gauge theory and the conformal block of 2 dimensional conformal field theory. The AGT relation predicts that we can express the Nekrasov partition function as the inner product of special states on conformal field theory side. We showed how the defining relations of these special states change, when there are matter fields in 4 dimensional SU(3) supersymmetric gauge theory. We also succeeded in describing the defining relations as a result of arising an irregular singularity from the confluence of two regular singularities on the Riemann surface on which conformal filed theory is defined.

Free Research Field

数理物理学