Matrix Model of Chern-Simons Matter Theories Beyond The Spherical Limit
Abstract
A class of matrix models which arises as partition function in U(N) Chern-Simons matter theories on three sphere is investigated. Employing the standard technique of the 1/N expansion we solve the system beyond the planar limit. In particular we study a case where the matrix model potential has 1/N correction and give a general solution thereof up to the order of 1/N^2. We confirm that the general solution correctly reproduces the past exact result of the free energy up to the order in the case of pure Chern-Simons theory. We also apply to the matrix model of N=2 Chern-Simons theory with arbitrary numbers of fundamental chiral multiplets and anti-fundamental ones, which does not admit the Fermi gas analysis in general.
Keywords
Cite
@article{arxiv.1610.06471,
title = {Matrix Model of Chern-Simons Matter Theories Beyond The Spherical Limit},
author = {Shuichi Yokoyama},
journal= {arXiv preprint arXiv:1610.06471},
year = {2019}
}
Comments
1+29 pages, 2 figures, v2: some improvements, figures added, v3: genus half loop equation solved, calculation for confirmation of the solution, further discussion, improvements, references added, v4: minor improvements, a new example, a reference added, published version