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

Abstract

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 $\mathrm{U}(N_1{)}_{k_1}\times \mathrm{U}(N_2{)}_{k_2}$, then the resolvents can be obtained in a more explicit form than in the general cases.

44 pages, 7 figures

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Cited by in corpus (14)

• Exact results on ABJ theory and the refined topological string
• M-theoretic matrix models
• ABJM Wilson Loops in Arbitrary Representations
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Instanton Effects in Orbifold ABJM Theory
• Localization at large N in Chern-Simons-matter theories
• Holographical Description of BPS Wilson Loops in Flavored ABJM Theory
• The large-N partition function for non-parity-invariant Chern-Simons-matter theories
• Subleading corrections to the $S^3$ free energy of necklace quiver theories dual to massive IIA
• Cubic constraints for the resolvents of the ABJM matrix model and its cousins
• Supersymmetry Breaking and Planar Free Energy in Chern-Simons-matter Theories
• Linear Chern-Simons-matter Theories in the Planar Limit
• Notes on Planar Resolvents of Chern-Simons-matter Matrix Models
• Strong Coupling Limit of A Family of Chern-Simons-matter Theories