Matrix model of Chern–Simons matter theories beyond the spherical limit

A class of matrix models that arises as a partition function in U(N) Chern–Simons matter theories on the three-sphere is investigated. Employing the standard technique of 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/N². 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 Fermi gas analysis in general