A Systematic Study on Matrix Models for Chern-Simons-matter Theories

We investigate the planar solution of matrix models derived from various Chern-Simons-matter theories compatible with the planar limit. The saddle-point equations for most of such theories can be solved in a systematic way. A relation to Fuchsian systems play an important role in obtaining the planar resolvents. For those theories, the eigenvalue distribution is found to be confined in a bounded region even when the 't Hooft couplings become large. As a result, the vevs of Wilson loops are bounded in the large 't Hooft coupling limit. This implies that many of Chern-Simons-matter theories have quite different properties from ABJM theory. If the gauge group is of the form ${\rm U}(N_1)_{k_1}\times{\rm U}(N_2)_{k_2}$, then the resolvents can be obtained in a more explicit form than in the general cases.

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