From Chern-Simons Theory To M-Theory

2018 Fiscal Year Final Research Report

• Project/Area Number: 26400245
• 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: Osaka City University (2015-2018); Nagoya University (2014)
• Principal Investigator: Moriyama Sanefumi 大阪市立大学, 大学院理学研究科, 准教授 (80402452)
• Project Period (FY): 2014-04-01 – 2019-03-31
• Keywords: M理論 / チャーン・サイモンズ理論 / 行列模型 / 可積分階層 / 量子曲線

Outline of Final Research Achievements

M-theory is a mysterious 11-dimensional theory which is considered to unify all perturbative 10-dimensional string theories non-perturbatively. The field theory that describes the worldvolume of multiple M2-branes is recently identified by Aharony, Bergman, Jafferis and Maldacena. After applying the localization technique for supersymmetric correlators, the partition function and one-point functions of the supersymmetric Wilson loops are reduced to matrix models. The ABJM matrix model was studied extensively in previous works. Here through the generalization of the matrix model we find many interesting relations characterizing the M2-brane physics. Our results include integrability, the open/closed duality, the correspondence between quantum curves and generalizations of the ABJM matrix model, and the relation between the orientifold projection of the matrix model and the chiral projection of the associated quantum mechanics.

Free Research Field

弦理論

Academic Significance and Societal Importance of the Research Achievements

11次元M理論は10次元弦理論を統一すると期待されているが、これまでM理論に関する知見は少なかった。本研究では、ABJM行列模型とその拡張模型の研究を通じて、M2ブレーンに関する理解を大きく深めた。特にABJM行列模型とその拡張模型の間に存在するさまざまな関係式はM理論の豊かな数理構造を示唆しており、最終的にM2ブレーンの超対称性を保つさまざまな背景幾何をまとめた「M理論の地図」に例外群と可積分性から生成される対称性が作用していることがわかる。この対称性の構造を通じて謎に包まれたM理論が解明され、M理論が精密に定式化されることが期待される。