Jacobi-Trudi Identity in Super Chern-Simons Matrix Model

Symmetry Integrability and Geometry-Methods and Applications

article

Tomohiro Furukawa¹  Sanefumi Moriyama¹ 

[1] Department of Physics, Osaka City University

关键词: Jacobi–Trudi identity;    ABJM theory;    Chern–Simons theory;    matrix model;    integrable system;   

DOI  :  10.3842/SIGMA.2018.049

来源: National Academy of Science of Ukraine

【 摘 要 】

It was proved by Macdonald that the Giambelli identity holds if we define the Schur functions using the Jacobi-Trudi identity. Previously for the super Chern-Simons matrix model (the spherical one-point function of the superconformal Chern-Simons theory describing the worldvolume of the M2-branes) the Giambelli identity was proved from a shifted version of it. With the same shifted Giambelli identity we can further prove the Jacobi-Trudi identity, which strongly suggests an integrable structure for this matrix model.

【 授权许可】

Unknown